Fussy baby at night due to…?

Im currently breastfeeding my 2mo baby girl and she tends to be fussy at night. Keep latch and unlatch and will fuss & cry. Sometimes this last for hours that i jus end up giving her EBM or formula milk so that she can sleep and i can rest too. How to strike a balance between wanting to feed my baby & not risking my milk supply dropping? Now baby starting to catnap during bedtime & will only sleep long stretch after midnight. By then im so exhausted already :(