I know that augmented intervals within part writing in both minor and major keys is forbidden but what about diminished intervals? For example if I we're in e minor and in 3/4 time and I'm writing a SATB. If I start a bar with a root position iv chord that is a minor and I have an a in the bass, e in the tenor, c in the alto and e in the soprano then the next chord is f# minor in first inversion where I have a in the bass, f# in the tenor, c in the alto and f# in the soprano then the next chord is V which is b major and I have b in the bass, f sharp in the tenor, b in the alto and d sharp in the soprano. My question is with a ii6(diminished)-V progression is it possible to avoid augmented/ diminished intervals? Is it correct to bring the f sharp in the soprano on the second beat like I did to a d sharp in the soprano on the third beat?
Your confusion concerning this issue stems from your incorrect voice leading. In the scenario you provided, you have parallel octaves between the first and second chord, which not only makes awkward voice leading for the third chord, but also leads to incorrect doubling for the second chord.
When using a diminished chord, it is better to double the third of the chord, never the root (as it is usually a leading tone.) Doubling the leading tone makes everyone cringe.
In your example, it would be much better to leave the soprano on E4, which gives you a iim7b5 (6/5) - in other words, a half-diminished, first-inversion f#m7 chord, which is extremely common in Bach's chorales. Making that simple change smooths out the voice leading and allows you to proceed to V with little fuss.
If you study Bach's chorales (and you should! and you should play through them!) you'll see that he uses a lot of passing tones to facilitate smooth voice leading, resolve dissonances, and anticipate suspensions.