Look up thunderbird archery and they sell a paint pen kit that comes in black or white. Won’t run, bleed, or fade then re shoot the area with a couple coats of thunderbird finish.
#2 bobbly lobby extra fine paint pen.
#3 calligraphy pen and India ink.
But first get on the horn with BW and ask what type of finish they use and see if they can re spray that area for you after you tell them what you want. They should be willing to do that for you. If not then find a local bowyer and see if he can touch up your finish in a spot.
Hope this helps