• Using Object#entries, get the key-value pairs of items
• Using Array#filter, iterate over the above array
• In each iteration, check if the current item has a key starting with qty_ whose value is not empty. You can do this using Object#keys, Array#some, and String#startsWith.
• Using Object#fromEntries, convert the filtered pairs to an object again.

const obj = {
  items: {
    1: {qty_auth: "", resolution: "4", status: "", order: "1495"},
    5: {qty_sized: "1", resolution: "4", status: "", order: "1485"}
  }
};

obj.items = Object.fromEntries(
  Object.entries(obj.items)
  .filter(([_, item]) =>
    Object.keys(item).some(key => key.startsWith('qty_') && item[key])
  )
);

console.log(obj);

You're talking about an array, but using curly brackets instead of square brackets. For filter() to work it would have to look like:

mydata = {
   items: [
      {qty_auth: "", resolution: "4", status: "", order: "1495"},
      {qty_sized: "1", resolution: "4", status: "", order: "1485"}
   ]
}

Assuming it is an actual array there's still a problem with "const mydatadata.items", or at least it throws an error for me because mydatadata is not initialized. Unless it's a typo and it should be mydata, but then you'd be redeclaring it. So depending on what you want:

mydata.items = mydata.items.filter((o) =>
        Object.keys(o).some((k) => k.startsWith("qty") && o[k])
);

or

let mydatadata = {};
mydatadata.items = mydata.items.filter((o) =>
        Object.keys(o).some((k) => k.startsWith("qty") && o[k])
);

Furthermore you're storing the result in mydatadata but you're logging the variable result. So depending on the previous answer:

console.log(mydatadata);

or

console.log(mydata);

Here's a fiddle: https://jsfiddle.net/b57qa82d/

You should probably just be using an array rather than an object. It's not really clear from your question what structure you need as you keep changing the terminology to describe your data. For example: "Now mydata.items has an array set" but your code says that it should be object with keys, not an array.

So I suggest: get your data in an array, and filter it by iterating over each object's entries and checking to see if any of the keys starting with "qty" has a value that isn't an empty string. You can then assign that filtered array to myObject.items.

const data = [
{ "qty_sized": "0", "resolution": "5", "status": "", "order": 2 },
{ "qty_auth": "", "resolution": "5", "status": "", "order": 3 },
{ "qty_auth": "1", "resolution": "5", "status": "", "order": 1342 },
{ "qty_sized": "", "resolution": "2", "status": "", "order": 1 },
{ "qty_sized": "1", "resolution": "1", "status": "", "order": 142 }];

const filtered = data.filter(obj => {
  return Object.entries(obj).find(([key, value]) => {
    return key.startsWith('qty') && value;
  });
});

const myObject = { items: filtered };

console.log(myObject);

Additional documentation

• Object.entries

• find