How can I find all the elements in javaScript array that start with certain letter

Three things:

• You want to split by ', ', not ','
• indexOf doesn't take a regex, but a string, so your code searches for a literal ^. Use search if you want to use regular expressions.
• indexOf (and search) do return the index where they find the sought-after term. You'll have to compare that to your expectation: == 0. Alternatively, you can use the regex test method which returns a boolean.

alert('apple, orange, apricot'.split(', ').filter(function(item, index) {
    return item.indexOf('a') == 0; 
}));
alert('apple, orange, apricot'.split(', ').filter(function(item, index) {
    return /^a/.test(item); 
}));

You have to trim the spaces from the item before checking.

Regex to check if start with: ^a

var fruit = 'apple, orange, apricot'.split(',');
fruit = $.grep(fruit, function (item, index) {
    return item.trim().match(/^a/);
});
alert(fruit);

Other solution:

var fruits = [];
$.each(fruit, function (i, v) {
    if (v.match(/^a/)) {
        fruits.push(v);
    }
});
alert(fruits);

You can use charAt like so :

var fruit = 'apple, orange, apricot'.split(', ');
  fruit = $.grep(fruit, function(item, index) {
  return item.charAt(0) === 'a';
});
alert(fruit);