ECMAScript 6 introduced String.prototype.includes:

const string = "foo";
const substring = "oo";

console.log(string.includes(substring)); // true

String.prototype.includes is case-sensitive and is not supported by Internet Explorer without a polyfill.

In ECMAScript 5 or older environments, use String.prototype.indexOf, which returns -1 when a substring cannot be found:

var string = "foo";
var substring = "oo";

console.log(string.indexOf(substring) !== -1); // true

String.prototype.includes() has something close to this functionality, as argument 2 is taken as the start position for searching.

If you want to search at, not after, a specific index, you can write a function that takes the string, creates a slice of it, and checks if that slice matches

function substring_at(string, substring, position) {
  let slice = string.slice(position, position + substring.length)
  
  // Triple equals removes type coercion support, and is slightly faster
  return slice === substring
}

I've tested it with your examples and all seems well.