How experienced at pistol shooting are you?
Does the gun shoot low, or low-and-left? (I assume that you're right-handed. If you're left-handed: low-and-right?)

It may be a matter of your own technique, since most pistols are pretty well regulated before they leave the factory.

I am right handed and I am fairly new to shooting handguns. I was grouping directly over the bullseye. When I aimed about three inches high I was able to put all shots in the bullseye, with most of holes touching each other.

I have wondered if it was my technique, but I was able to shoot a full size M&P in .40, a Glock 22 in .40, an XDm in .40 and a S&W .357 all during the same trips to the range and all the shots went where I expected them. I had 2 other individuals shoot mine, and they had a similar problem with it shooting low. None of us are great shots, but since I didn't have problems with the other guns I am suspecting it is mine. I shot mine first, then theirs and then came back to mine. I will pay more attention on my next trip to the range.

Not trying to sound like a jerk, honestly, but move the target out further. You may find that at 7 to 10 yards (more typical ranges for hand-gunners) things are better. The POI climbs in the early part of it's trajectory. I've found that Handguns sighted in for 7 yds shoot noticeably higher at 10 & 15 yards. Worst case? Nothing. It's free to try.

Bench rest the pistol @ 7 to 10 yards and see where you are hitting. This should take out as much human error as possible. If it's still shooting low you may need a lower front sight or higher rear sight. I've experienced personally during a bench test shooting my 92 which was hitting low right off the bench, drifted the rear sight left and it brought it center and up.

Combat site hold, front site covers the target.

Good advice from Overkill, denner, and thndrchiken.

Pistols are normally zeroed for 25 yards. The bullet is still rising at seven-to-ten yards, high at 15, and spot-on at 25.
That may be your problem.