All you need is Array.reduce with Array.filter

If you want to select only those object whose selected property is true, irrespective of what value id holds then can try below snippet.

let arr = [
    {id: 'a660f87e-476d-493b-a220-31aff8cf764c', selected: true},
    {id: '1e8284a5-6ba3-48c0-b8ac-f6ffae55b44e', selected: true},
    {id: '1e8284a5-6ba3-48c0-b8ac-f6ffae55b44f', selected: false},
    {id: '1e8284a5-6ba3-48c0-b8ac-f6ffae55b44e', selected: false},
    {id: 'a660f87e-476d-493b-a220-31aff8cf764c', selected: true}
]


arr = Object.values(arr.reduce( (a, b) => {
    a[b.id] = a[b.id] ? a[b.id] : b ;
    return a;
}, {})).filter(a => a.selected === true)

console.log(arr);

You can provide you check just like if condition to filter

So two action items in your questions.

1. Get the items only if selected is true
2. If the selected id already available in new array then not required to include again(Like you want unique array).

you can achieve it like below.

let tmp = [{id: '1', selected: true},
{id: '2', selected: true},
{id: '1', selected: true}];

var newArr = [];
var tmp1 = tmp.map((itm) => {
  var t = newArr.map(a => a.id);
    if(t.indexOf(itm.id) == -1 && itm.selected) {
    newArr.push(itm);
  }
});
console.log(newArr);

So basically you want to remove object with selected: false from the array, right?

Maybe you can use a loop to remove the object with selected: false.

let _array = [{
        id: 'a660f87e-476d-493b-a220-31aff8cf764c',
        selected: true
    },
    {
        id: '1e8284a5-6ba3-48c0-b8ac-f6ffae55b44e',
        selected: true
    },
    {
        id: 'a660f87e-476d-493b-a220-31aff8cf764c',
        selected: false
    }
];
let temp_array = [];
_array.forEach((object, index) => {
    if (object.selected == false && hasDuplicate(object.id) == true) {
        _array.splice(index, 1);
    }
});

function hasDuplicate(id) {
    // function for finding if the element has a duplicate.
    _array.forEach(object => {
        temp_array.push(object.id)
    }); // A temporary array for storing all the ids.
    var indexes = [],
        i = -1;
    while ((i = temp_array.indexOf(id, i + 1)) != -1) {
        indexes.push(i);
    } // Finds indexes of all object with same id
    if (indexes.length > 1) {
        return true;
    } // if has more than 1 index it returns true (hasDuplicate = true)

    return false; 
}

In your question there is no comma (,) b/w the elements so please edit your question.