why does a green spotted puffer nibble on the fish fins?

You did not do your research before purchasing the green spotted puffer!! If you had researched the fish, you would know that GSPs require brackish water in their juvenile stage and eventually need a full marine environment when fully grown. Also, GSPs need to be kept in specimen tanks as they are highly territorial. The GSP will eventually eat every other fish in your tank unless it dies first due to being kept in inappropriate water conditions. Also, GSPs must be fed snails and/or other crustaceans to keep their "beak" filed. The beak is actually the teeth of the GSP which "fuses" together.

You need to purchase a 29 - 55 gallon tank for your GSP immediately and set it up properly for this fish. Otherwise, you should return the fish.

You can get a tank separator and separate the puffer from the other fish. You could also try and get another type of food for the puffer. Sometimes the fin nippers will stop after a while or the fish will learn to stay away from them. You could also try and just feed the puffer before you feed the other fish so that it gets enought to eat.

If all of this doesn't work then I suggest you give the puffer away for the sake of your other fish.

Grilled Chicken

you should take alll the fishes into a place them into a clean water but they need use only salt water , by useing salt water is you can use the out side water or you can pour some salt in the clean tank then clean the tank after pour the new salt water back to the tank and put the fishes back too. maybe the fishes will stop nipples each other.

its nature they do what they want to do.puffer are not supposed to be with tetra guppies and platies there saltwater