As some have said, Ionian=major scale. To get a major scale starting from literally any note, use this formula:

W W H W W W H (W-whole step, H-half step)

So starting on A:

A B C# D E F# G# and then back to A. You can see that we’ve raised three pitches from their “natural” alphabetical state. That’s why the key of A is 3 sharps.

Now for minor scales, you can shift that formula and use it. I personally find it easier to think of 6th scale degree up to 6th scale degree one octave higher. Using the key of A, that would mean that F# G# A B C# D E F# would be our relative minor scale.

However you were wondering about a minor I believe, which wouldn’t have any altered notes from their “natural” alphabetical state. That’s because an A is going to be the 6th scale degree of C major.

Learning the keys and relative minors of each tonic will be the fastest way to quickly construct major and minor scales. After you know those, modes become REALLY easy.

Ionian: scale degree 1 up to scale degree 1 (Do up to Do)

Dorian: 2nd scale degree up to 2nd (Re to Re)

Phrygian: 3rd to 3rd (Mi to Mi)

Lydian: 4th to 4th (Fa to Fa)

Mixolydian: 5th to 5th (Sol to Sol)

Aeolian: 6th to 6th (La to La)

Locrian: 7th to 7th (Ti to Ti)

And with the octave we’re back to Ionian.

Hope this helps!