I had same gun for my youngest,When he started turkey hunting.
No unfortunately they dont make any brand of hevi shot,in 20 ga.2 3/4"shells.Just in a 3" shell.
Ive patterned the Winchester super x HIGH BRASS #4 AND THE #5 2 3/4" shells.They are just lead shot.But my youngest has taken toms,hens etc.One shot stone dead out to 30-35 yrds!It patterns very well,Considering its a 20 ga.with only a 2 3/4"shell.
I think its like $16 for 25 shells.So u have plenty to pattern,and hunt with.
Hope this helps,and good luck...