Generalizing Afanasii Kurakin's answer, we have:

function replaceAt(str, index, ch) {
    return str.replace(/./g, (c, i) => i == index ? ch : c);
}

let str = 'Hello World';
str = replaceAt(str, 1, 'u');
console.log(str); // Hullo World

Let's expand and explain both the regular expression and the replacer function:

function replaceAt(str, index, newChar) {
    function replacer(origChar, strIndex) {
        if (strIndex === index)
            return newChar;
        else
            return origChar;
    }
    return str.replace(/./g, replacer);
}

let str = 'Hello World';
str = replaceAt(str, 1, 'u');
console.log(str); // Hullo World

The regular expression . matches exactly one character. The g makes it match every character in a for loop. The replacer function is called given both the original character and the index of where that character is in the string. We make a simple if statement to determine if we're going to return either origChar or newChar.

You could try

var strArr = str.split("");

strArr[0] = 'h';

str = strArr.join("");

You could try

var strArr = str.split("");

strArr[0] = 'h';

str = strArr.join("");

Check out this function for printing steps

steps(3)
//       '#  '
//       '## '
//       '###'

function steps(n, i = 0, arr = Array(n).fill(' ').join('')) {
  if (i === n) {
    return;
  }

  str = arr.split('');
  str[i] = '#';
  str = str.join('');
  console.log(str);

  steps(n, (i = i + 1), str);
}

Using the spread syntax, you may convert the string to an array, assign the character at the given position, and convert back to a string:

const str = "hello world";

function replaceAt(s, i, c) {
  const arr = [...s];  // Convert string to array
  arr[i] = c;          // Set char c at pos i
  return arr.join(''); // Back to string
}

// prints "hallo world"
console.log(replaceAt(str, 1, 'a'));

You can extend the string type to include the inset method:

String.prototype.append = function (index,value) {
  return this.slice(0,index) + value + this.slice(index);
};

var s = "New string";
alert(s.append(4,"complete "));

Then you can call the function:

this is easily achievable with RegExp!

const str = 'Hello RegEx!';
const index = 11;
const replaceWith = 'p';

//'Hello RegEx!'.replace(/^(.{11})(.)/, `$1p`);
str.replace(new RegExp(`^(.{${ index }})(.)`), `$1${ replaceWith }`);

//< "Hello RegExp"

You can concatenate using sub-string function at first select text before targeted index and after targeted index then concatenate with your potential char or string. This one is better

const myString = "Hello world";
const index = 3;
const stringBeforeIndex = myString.substring(0, index);
const stringAfterIndex = myString.substring(index + 1);
const replaceChar = "X";
myString = stringBeforeIndex + replaceChar + stringAfterIndex;
console.log("New string - ", myString)

or

const myString = "Hello world";
let index = 3;
myString =  myString.substring(0, index) + "X" + myString.substring(index + 1);

Here is a version I came up with if you want to style words or individual characters at their index in react/javascript.

replaceAt( yourArrayOfIndexes, yourString/orArrayOfStrings ) 

Working example: https://codesandbox.io/s/ov7zxp9mjq

function replaceAt(indexArray, [...string]) {
    const replaceValue = i => string[i] = <b>{string[i]}</b>;
    indexArray.forEach(replaceValue);
    return string;
}

And here is another alternate method

function replaceAt(indexArray, [...string]) {
    const startTag = '<b>';
    const endTag = '</b>';
    const tagLetter = i => string.splice(i, 1, startTag + string[i] + endTag);
    indexArray.forEach(tagLetter);
    return string.join('');
}

And another...

function replaceAt(indexArray, [...string]) {
    for (let i = 0; i < indexArray.length; i++) {
        string = Object.assign(string, {
          [indexArray[i]]: <b>{string[indexArray[i]]}</b>
        });
    }
    return string;
}

Here is my solution using the ternary and map operator. More readable, maintainable end easier to understand if you ask me.

It is more into es6 and best practices.

function replaceAt() {
  const replaceAt = document.getElementById('replaceAt').value;

  const str = 'ThisIsATestStringToReplaceCharAtSomePosition';
  const newStr = Array.from(str).map((character, charIndex) => charIndex === (replaceAt - 1) ? '' : character).join('');

  console.log(`New string: ${newStr}`);
}

<input type="number" id="replaceAt" min="1" max="44" oninput="replaceAt()"/>

My safe approach with negative indexes

/**
 * @param {string} str 
 * @param {number} index 
 * @param {string} replacement 
 * @returns {string}
 */
static replaceAt (str, index, replacement)
{
    if (index < 0) index = str.length + index
    if (index < 0 || index >= str.length) throw new Error(`Index (${index}) out of bounds "${str}"`)
    return str.substring(0, index) + replacement + str.substring(index + 1)
}

Use it like that:

replaceAt('my string', -1, 'G') // 'my strinG'
replaceAt('my string', 2, 'yy') // 'myyystring'
replaceAt('my string', 22, 'yy') // Uncaught Error: Index (22) out of bounds "my string"

You can use the following function to replace Character or String at a particular position of a String. To replace all the following match cases use String.prototype.replaceAllMatches() function.

String.prototype.replaceMatch = function(matchkey, replaceStr, matchIndex) {
    var retStr = this, repeatedIndex = 0;
    for (var x = 0; (matchkey != null) && (retStr.indexOf(matchkey) > -1); x++) {
        if (repeatedIndex == 0 && x == 0) {
            repeatedIndex = retStr.indexOf(matchkey);
        } else { // matchIndex > 0
            repeatedIndex = retStr.indexOf(matchkey, repeatedIndex + 1);
        }
        if (x == matchIndex) {
            retStr = retStr.substring(0, repeatedIndex) + replaceStr + retStr.substring(repeatedIndex + (matchkey.length));
            matchkey = null; // To break the loop.
        }
    }
    return retStr;
};

Test:

var str = "yash yas $dfdas.**";

console.log('Index Matched replace : ', str.replaceMatch('as', '*', 2) );
console.log('Index Matched replace : ', str.replaceMatch('y', '~', 1) );

Output:

Index Matched replace :  yash yas $dfd*.**
Index Matched replace :  yash ~as $dfdas.**

I se this to make a string proper case, that is, the first letter is Upper Case and all the rest are lower case:

function toProperCase(someString){
    
    return someString.charAt(0).toUpperCase().concat(someString.toLowerCase().substring(1,someString.length));
    
};

This first thing done is to ensure ALL the string is lower case - someString.toLowerCase()

then it converts the very first character to upper case -someString.charAt(0).toUpperCase()

then it takes a substring of the remaining string less the first character -someString.toLowerCase().substring(1,someString.length))

then it concatenates the two and returns the new string -someString.charAt(0).toUpperCase().concat(someString.toLowerCase().substring(1,someString.length))

New parameters could be added for the replacement character index and the replacement character, then two substrings formed and the indexed character replaced then concatenated in much the same way.

Dermot

"hello world".replace(/(.{3})./, "$1h")
// 'helho world'