I have an Apple Watch that needs a battery replacement because it doesn’t hold the battery. I had it for only 3 years! How much should pay for replacement of battery? I don’t have apple care

Apple Support offers this link where you can check the cost of Apple replacing that battery. You would not want anyone else replacing that battery.

Apple Watch Service & Repair - Apple Support

I took a guess at which model you have and this is what I found:

Apple will not replace a battery on your Apple watch, it will only suggest you to get a new watch, what you can do is you can go to the repair store and ask if they can replace a battery on it+ as it says up there you have an Apple watch series 2 it’s actually a very old Apple Watch