I recall the Gennessee (spelling?) Cream Ale and Ballantine but not the Maxmimus. Back then there was also the off brand from I think the Coors folks called "Strohs." That was pretty good for the tier just up from the bottom of the barrel.
I remember being very young and seeing Genesee signs all over Pennsylvania and New York.
My grandparents(fathers side)lived in north central Pennsylvania probably about 45 minutes from the New York border and those Genesee signs were everywhere. Gas stations, convenient stores, sides of barns everywhere.
I remember being 5/6 years old asking my dad what it was...I didn't even know it was beer...
Then I was 18 fishing in upstate NY and a place in Hancock NY had it on the shelf...I grabbed a 6 pack went to pay for it and the lady behind the counter goes are you 21? I said no I'm 18 but I always wanted to try this. She said ok....and a pack of Marlboros of course.