I have a summons to appear in family court for my son's father who wants to have his support lowered. I'm sure it will be granted as he is currently incarcerated, I don't want to waste my time, since I have no argument, so can I just not show up? What could I say or do to make a difference?

Look at it this way... not showing up makes you look bad to the court. Its worth an afternoon of your time for that reason alone.

This has been asked and answered - https://www.askmehelpdesk.com/family-law/how-petition-fathers-rights-ny-state-553764.html#post2706046.

Yes, I would show up just to prove that I'm interested.

How long will he be in jail? If you want a no contact order on behalf of your son, this is the time to request it.