I think that the attribution you have is pretty accurate so far.
The green on the obverse does not look to be bronze disease and appears stable. Most people will leave well alone.
I think that with the photos you have we can narrow the attribution down slightly further. You can make out that there is a dot in the centre field.
Constantius II - AE3
Obv:- D N CONSTANTIVS P F AVG, Pearl diademed, draped, cuirassed bust right
Rev:- FEL TEMP RE-PARATIO, Helmeted soldier to left, shield on left arm, spearing falling horseman; shield on ground at right. Horseman wears helmet and falls forward reaching towards emperor
Minted in Constantinople (dot //CONS?). 15th March A.D. 351 - Winter A.D. 354 (dating suggested by RIC)
Reference:- RIC VIII Constantinople 121
The question mark above is because I cannot make out the letter(s) following the CONS in exe. This would allow the identification of the workshop / officinal that produced the coin.
Here are a couple of mine from the same issue.
Workshop = IA = 11

This one is subtly different in that the reverse legend has a different break in it with R-EP rather than RE-P. The R-EP is slightly scarcer but doesn't change the attribution.
Workshop = S (Digamma) = 6

Hopefully this additional information is of interest.
Regards,
Martin