Advice for low voltage electrolysis system please
You want a bench power supply

A bench power supply is a box of electronics you plug into the mains, and provides an adjustable current and voltage. They are versatile and easy to use, especially for beginners. They are also generally useful as pieces of equipment to have in the lab as you learn more about electronics.

Here is an example of what they look like: Tenma 30V 3A supply on Farnell. This isn't a recommendation of what to buy though, you'll need to work out a bit more detail of what you need.

It looks like you're trying to make hydrogen. If so, each amp that the power supply can provide will make very roughly 0.1ml of hydrogen per second, assuming the electrodes are large enough and there is enough overpotential. So you can work out how much current you need from how much hydrogen you want and how long you can wait.