You are looking for that unicorn but it doesn’t really exist with any certainty. Sure a few top colleges offer a very limited number of merit scholarships (e.g. Duke, Vanderbilt) but highly unlikely your student will get one since they give so few out.
Some of the mid tier UCs give some merit money (I think my D got 8K/yr at UC Davis before she pulled her app) but the COA would have still been 100K+. UCB and UCLA give regents scholars but they are only 2K a year. If looking at CSUs, Cal Poly SLO and SDSU are becoming very good, affordable alternatives for in-state students.
How much can you afford without merit? That would help us find a good college for him.