For a melody harmonization, I wrote a 2 bar bassline using half notes with scale degrees ^1 ^7 3^ and ^5 and wanted to write chords for these bass tones. For the first bass note I chose the I chord. For ^3 I wanted to use iii and for ^5 a V7 to take me back to tonic. For 7^ (second chord) I thought about just having the same I chord but with its 7th in the bass. I am currently learning harmony and voice leading and this is not a chord that has been taught to me. In fact such a bassline seems to not fit with the standard rules I have learned so far. How would a classical composer view this kind of chord progression? Would the 2nd chord be a I42? Although to be that chord wouldnt the ^7 need to resolve down to ^6?
EDIT: Is it possible to consider this a progression in C#m aeolian or E and not in A major? Yes the cadence does seem to point back to A as the tonic but the bassline here does seems to work from a functional theory perspective if we consider that the E at the end of the progression is not a dominant but a secondary dominant.