I have a 5mm Sheridan (.20inch)and shoot pellete from:
https://www.pyramydair.com/ammo/air-gun-ammo/pellets
Iron sights of scope? Some of the optics air guns come with are pretty poor.
I have a Game and it seems happy with most pellets.
You may need to try a variety to find one your rifle “likes”.
The link provided by sasquatch has a number of sampler packs, that ought to make it easier to find a pellet your gun likes.
Benjamin pellets are good.
Are the pellets making nice round holes, or are they oblong or hitting sideways?
Could you give a description of the pellets? Perhaps from the label?
Competition distance is typically 10 meters (33 feet).
There are competition pellets for a price.
RWS makes probably the best pellets.
Available at any major supplier.
Pointed pellets are nice for penetration.
The RWS pellet rifles are unsurpassed!
Eley pellets (UK) - best in the world. getting groups the size of a postage stamp or less at 10 meters with our Feinwerkbau 900 iron sighted match rifle.
My pet springer groups flat-nosed H&N Match Rifle pellets the best, but it will handle many other "field" pellets acceptably. My experiences with Crosman and Daisy pellets have generally been disappointing.
.177 airguns are like .22 rimfires in that they are often fussy about what you use, and airguns in general require greater consistency in hold and even loading procedures (such as whether or not a pellet seater of some sort is used, depth of pellet insertion, etc). I can waste the best pellets in the world if I don't hold and follow through consistently.
Crosman Premiers are actually very decent and not expensive. I’ve found Daisy pellets to be garbage. High powered break barrel air rifles are not the easiest to shoot accurately. Do a search for artillery hold.
I should have added almost all guns are sensitive to pellet weight. By an assortment of weights to find what your gun likes.
Is this a break barrel and are you using a scope or the iron sights? The iron sights are mounted on the barrel and should shoot consistently. If you mount a scope it’s not fixed to the barrel and every time you lever the barrel, you can wind up with a different aim point with respect to the scope.
I've tried 10 or so different types from different manufacturers. Gamo .177 Rocket is the best all around. I have 1450 fps Gamo
You should have spent $30 on a daisy red rider bb gun. A better first rifle for a boy, Lots more fun, cheaper and easier to load and shoot than a gamo.. And it will hit a soda can at 10 meters 100/100 times.
I put a different scope on mine and sighted it in. I can group about an inch to 2 inches at 50 yards. Further than that it’s a crap shoot.
Use the raptor pellets. That’s what we use in ours.
You need to put at least 100 pellets through it to break it in.
Gamo, Beeman, and RWS have served me well. I have an RWS model 134 made in West Germany.