You already know that a pet for a three-year-old is really a pet Mama takes responsibility for. My granddaughters have a Beta, and my DIL says he's rather low maintenance. Those girls are older than your son, so they all take care of him (I think it's a him) together. He's #2 Beta - #1 lived only a week, and it was traumatic. The girls had to learn quickly about short life spans.
Low maintenance is not NO maintenance. He's a living thing and needs attention and care. I'm informed by my grans that their little guy has a personality and recognizes them when they look at him.
AN ASIDE: Some readers may be thinking, "When ARE children old enough to take care of a pet by themselves?" I imagine it varies with the child and the family. My children grew up with dogs and cats, but didn't really have the responsibility for them (just the jobs). When they were in junior high we started letting them have pets that were their sole responsibility, if they were interested. They had to do research on the care of the animal before this addition to the family was okayed. Child #1 got serious about fish, child #2 had a series of hamsters (she took beautiful care of them, but they just don't live very long), and child #3 had a lovely parakeet for several years. Child #4 was set on NOT copying his siblings; however, when he grew up he married a girl and a cat (they came as a set). The kitty has passed on, but they now have two friendly, well-behaved dogs as well as a beautiful baby girl. :^)