I want the count of double char occurring in a string, using JS regular expression

I don't know if it possible to achieve it only by using regular expressions but you can write a function such as:

function countOccurencies(text, pattern) {
  let index = 0;
  let count = 0;
  let find;
  while((find = text.substr(index).search(pattern)) >= 0) {
    index += find + 1;
    count++;
  }
  return count;
}

// You can use it like this:
let occ;
occ = countOccurencies('caaab', /aa/g); // 2
occ = countOccurencies('caaab', 'aa');  // 2

You could use the following expression: /(.)(?=\1)/g

Short explanation:

• (.) is a capture group; it captures any character except newlines
• \1 is a backreference to the first capture group (the (.))
• (?=\1) creates a positive lookahead for that backreference \1 (without consuming characters)
• The g option at the end of the regex indicates that all matches should be returned instead of just the first one.

The final regex match result will contain all characters that are followed by that same character.

let regex = /(.)(?=\1)/g
let a1 = 'caaab'
let r1 = a1.match(regex) // [ 'a', 'a' ]
let a2 = 'caaabbcdd'
let r2 = a2.match(regex) // [ 'a', 'a', 'b', 'd' ]

You will not get doubled characters in your regex matches, only single characters. But they can be easily doubled by using the Array.prototype.map function, because you know for sure that they are always followed by that same character in the search string.

let regex = /(.)(?=\1)/g
let a1 = 'caaab'
let r1 = a1.match(regex).map(ch => ch + ch) // [ 'aa', 'aa' ]
let a2 = 'caaabbcdd'
let r2 = a2.match(regex).map(ch => ch + ch) // [ 'aa', 'aa', 'bb', 'dd' ]

Newlines

The (.) capture group does not match doubled newlines. If you also want to include doubled newlines, you could add them in the capture group like this: (.|\n). The resulting code would look like this:

let regex = /(.|\n)(?=\1)/g
let a = 'caaab\nbbc\n\nddd'
let r = a.match(regex).map(ch => ch + ch) // [ 'aa', 'aa', 'bb', '\n\n', 'dd', 'dd' ]

Note on performance and maintainability

Regular expressions can have serious performance penalties. Furthermore, they are difficult to read and understand. As my answer might provide a valid solution for your problem using regular expressions, I advise not to use it. Creating a small function that provides the same result might be a lot more performant and clearer to understand, which eases future maintenance.

function getDoubleChars(searchString, includeNewlines = false) {
  let result = []
  let previousChar = ''

  for (let char of searchString) {
    if (char === previousChar) {
      if (char !== '\n' || includeNewlines) {
        result.push(char + char)
      }
    }

    previousChar = char
  }

  return result;
}

let a = 'caaab\nbbc\n\nddd'
let r = getDoubleChars(a) // [ 'aa', 'aa', 'bb', 'dd', 'dd' ]
let r = getDoubleChars(a, true) // [ 'aa', 'aa', 'bb', '\n\n', 'dd', 'dd' ]