I want to filter array of objects with a string that should match with a objects property key and should check that key value

I have an array of objects

const workSchedule = [
	{
		name: 'a',
		age: 21,
		workDays: {
			monday: {isavailable:true}, tuesday:{isavailable:false}, wednesday:{isavailable:true}, thursday:{isavailable:true}, Friday:{isavailable:false}
		}
	},
	{
		name: 'b',
		age: 22,
		workDays: {
			monday: {isavailable:false}, tuesday:{isavailable:false}, wednesday:{isavailable:true}, thursday:{isavailable:false}, Friday:{isavailable:false}
		}
	}
]

and I have a string variable which have a selected Day

 const day='Monday'

Now I want to check if the person A or B is available on monday or not?

Try like this,

<!-- begin snippet: js hide: false console: true babel: false -->

<!-- language: lang-js -->

  const workSchedule = [
    {
      name: "a",
      age: 21,
      workDays: {
        monday: { isavailable: true },
        tuesday: { isavailable: false },
        wednesday: { isavailable: true },
        thursday: { isavailable: true },
        friday: { isavailable: false },
      },
    },
    {
      name: "b",
      age: 22,
      workDays: {
        monday: { isavailable: false },
        tuesday: { isavailable: false },
        wednesday: { isavailable: true },
        thursday: { isavailable: false },
        friday: { isavailable: false },
      },
    },
  ];

  const day = "Monday";

  workSchedule.forEach((e) => {
    if (e.workDays[day.toLocaleLowerCase()]["isavailable"]) {
      console.log(e.name + " is available");
    } else {
      console.log(e.name + " is not available");
    }
  });

<!-- end snippet -->

Here is a way to achieve what you want, but you should try to write the code you have tried so far to reach your goal.

Also, think to be consistent in the variables names in your Object "Friday" the first letter is an upper case.

The first snippet is just to do what you asked, the second one is more reusable to have access to the availablePersons Array out of the function.

<!-- begin snippet: js hide: false console: true babel: false -->

<!-- language: lang-js -->

		const workSchedule = [
		  {
			name: 'a',
			age: 21,
			workDays: {
			  monday: { isavailable: true },
			  tuesday: { isavailable: false },
			  wednesday: { isavailable: true },
			  thursday: { isavailable: true },
			  friday: { isavailable: false }
			}
		  },
		  {
			name: 'b',
			age: 22,
			workDays: {
			  monday: { isavailable: false },
			  tuesday: { isavailable: false },
			  wednesday: { isavailable: true },
			  thursday: { isavailable: false },
			  friday: { isavailable: false }
			}
		  }
		];
		
		function getAvailablePersons(day){
			let lowercaseDay = day.toLowerCase();

			// Array to store available persons
			let availablePersons = [];

			workSchedule.forEach(person => {
			  if (
				person.workDays &&
				person.workDays.hasOwnProperty(lowercaseDay) &&
				person.workDays[lowercaseDay].isavailable
			  ) {
				availablePersons.push(person);
			  }
			});

			// Display available persons
			console.log(`available persons on ${day}: (${availablePersons.length})`);
			availablePersons.forEach(person => {
			  console.log(`- ${person.name}`);
			});
		}
		
		getAvailablePersons('Monday');
		getAvailablePersons('Wednesday');

<!-- end snippet -->

Here's a better and more reusable snippet Where you retrieve an Array of Objects that contains the available persons only, so you can realize other searches on those persons :

<!-- begin snippet: js hide: false console: true babel: false -->

<!-- language: lang-js -->

		const workSchedule = [
		  {
			name: 'a',
			age: 21,
			workDays: {
			  monday: { isavailable: true },
			  tuesday: { isavailable: false },
			  wednesday: { isavailable: true },
			  thursday: { isavailable: true },
			  friday: { isavailable: false }
			}
		  },
		  {
			name: 'b',
			age: 22,
			workDays: {
			  monday: { isavailable: false },
			  tuesday: { isavailable: false },
			  wednesday: { isavailable: true },
			  thursday: { isavailable: false },
			  friday: { isavailable: false }
			}
		  }
		];
		
		let availablePersons = [];
		let day = null;
		
		function getAvailablePersons(aDay){
			let lowercaseDay = aDay.toLowerCase();

			// Array to store available persons
			availablePersons = [];

			workSchedule.forEach(person => {
			  if (
				person.workDays &&
				person.workDays.hasOwnProperty(lowercaseDay) &&
				person.workDays[lowercaseDay].isavailable
			  ) {
				availablePersons.push(person);
			  }
			});
			return availablePersons;
		}
		
		function listPersons(day){
			// Display available persons
			day = day.toLowerCase();
			console.log(`available persons on ${day}: (${availablePersons.length})`);
			availablePersons.forEach(person => {
			  console.log(`- ${person.name}`);
			});
		}
		
		day = 'Monday';
		let personsOnMonday = getAvailablePersons(day);
		console.log(personsOnMonday);
		listPersons(day);
		
		day = 'Wednesday';
		let personsWednesday = getAvailablePersons(day);
		console.log(personsWednesday);
		listPersons(day);

<!-- end snippet -->

You can achieve this simply with filter method.

<!-- begin snippet: js hide: false console: true babel: false -->

<!-- language: lang-js -->

        const day = 'monday';
        const workSchedule = [
        {
            name: 'a',
            age: 21,
            workDays: {
                monday: {isavailable:true}, tuesday:{isavailable:false}, wednesday:{isavailable:true}, thursday:{isavailable:true}, Friday:{isavailable:false}
            }
        },
        {
            name: 'b',
            age: 22,
            workDays: {
                monday: {isavailable:false}, tuesday:{isavailable:false}, wednesday:{isavailable:true}, thursday:{isavailable:false}, Friday:{isavailable:false}
            }
        }
    ];

    
const available = workSchedule.filter(sch=> sch.workDays[day.toLowerCase()].isavailable === true);


console.log(available[0]);
console.log(available[0].name);

<!-- end snippet -->

First you should standardise your input data to make it consistent (friday instead of Friday, for example, and isAvailable instead of isavailable).

The answer depends on what kind of data you're expecting as output. This will inform how the data is meant to be queried and manipulated.

Here are a few examples.

1. Using filter and map to create an array of names we can assign to a variable called isAvailableOnMonday.

<!-- begin snippet: js hide: false console: true babel: false -->

<!-- language: lang-js -->

const workSchedule=[{name:"a",age:21,workDays:{monday:{isAvailable:!0},tuesday:{isAvailable:!1},wednesday:{isAvailable:!0},thursday:{isAvailable:!0},friday:{isAvailable:!1}}},{name:"b",age:22,workDays:{monday:{isAvailable:!1},tuesday:{isAvailable:!1},wednesday:{isAvailable:!0},thursday:{isAvailable:!1},friday:{isAvailable:!1}}}];
const day = 'Monday';

// Accepts the data and day as arguments
function finder(data, day) {

  // For each object in the data...
  return data.filter(obj => {

    // Destructure `name` and `workDays` from the object
    const { name, workDays } = obj;

    // Check to see if that day is available (making sure you
    // render the day string to lower case)
    return workDays[day.toLowerCase()].isAvailable;

  // Finally `map` over the returned array of objects and
  // extract their names into a new array
  }).map(obj => obj.name);

}

const isAvailableOnMonday = finder(workSchedule, day);
console.log(isAvailableOnMonday);

<!-- end snippet -->

2. In this example we're just using map to iterate over the data objects to return a new array of objects that describes if a particular day isAvailable.

<!-- begin snippet: js hide: false console: true babel: false -->

<!-- language: lang-js -->

const workSchedule=[{name:"a",age:21,workDays:{monday:{isAvailable:!0},tuesday:{isAvailable:!1},wednesday:{isAvailable:!0},thursday:{isAvailable:!0},friday:{isAvailable:!1}}},{name:"b",age:22,workDays:{monday:{isAvailable:!1},tuesday:{isAvailable:!1},wednesday:{isAvailable:!0},thursday:{isAvailable:!1},friday:{isAvailable:!1}}}];
const day = 'Monday';

// Accepts the data and day as arguments
function finder(data, day) {

  // For each object in the data...
  return data.map(obj => {

    // Destructure `name` and `workDays` from the object
    const { name, workDays } = obj;

    // Check to see if that day is available (making sure you
    // render the day string to lower case)
    const isAvailable = workDays[day.toLowerCase()].isAvailable;

    // Return a new object that specifies the name, day, and
    // availability as key/value pairs
    return { name, day, isAvailable };
  });
}

console.log(finder(workSchedule, day));

<!-- end snippet -->

Additional documentation

• Destructuring assignment

• toLowerCase

3. In this example, we're using reduce to create an object that places the names of people in an isAvailable array for a particular day.

<!-- begin snippet: js hide: false console: true babel: false -->

<!-- language: lang-js -->

const workSchedule=[{name:"a",age:21,workDays:{monday:{isAvailable:!0},tuesday:{isAvailable:!1},wednesday:{isAvailable:!0},thursday:{isAvailable:!0},friday:{isAvailable:!1}}},{name:"b",age:22,workDays:{monday:{isAvailable:!1},tuesday:{isAvailable:!1},wednesday:{isAvailable:!0},thursday:{isAvailable:!1},friday:{isAvailable:!1}}}];
const day = 'Monday';

// Accepts the data and day as arguments
function finder(data, day) {

  // For each object in the data...
  return data.reduce((acc, obj) => {

    // Destructure `name` and `workDays` from the object
    const { name, workDays } = obj;

    // Create an object key using the lowercase'd day value
    const key = day.toLowerCase();

    // Check to see if that day is available
    const { isAvailable } = workDays[key];

    // If the day doesn't exist as a key on the output object
    // add it and initialise it to an object with an empty
    // `isAvailable` array
    acc[key] ??= { isAvailable: [] };
    
    // The day _is_ available add the name to the `isAvailable`
    // array for that day
    if (isAvailable) acc[key].isAvailable.push(name);
    
    // Return the accumulator for the next iteration
    return acc;
  
  }, {});

}

console.log(finder(workSchedule, day));

<!-- end snippet -->