Where can I find subsidized senior housing in Sayreville NJ?

Start with your state's office on aging website (it may be called something else.) Also, go to the general State website and type in "subsidized housing." You should get a list of apartments that are dedicated to both seniors and/or low income.
Be careful, though, my Mom's subsidized apartment cost about the same as a regular apartment in her hometown. Also, occupants need to do a yearly "accounting" of their assets...such a hassle. Some apartments are great...ours here are lovely. Others are run by less than reputable people and resemble tenaments.
good luck