Blue Spot Puffer? Algae?

[naesco]

As you are having algae issues with your tank which are generally caused by lighting or water quality issues you should not consider putting more fish in your tank until everything stabilizes.

If you do you can expect more serious problems to develop.

[fishoholic]

Puffers will eat snails and shrimp, but usually leave corals alone. If it's a toby puffer you're thinking of they are known to nip the fins of tank mates.

[hillegom]

If you use RO water, you will have less problems with algae. As well, feed less.
How old and what size is the tank? How much nitrates do you have?