If the frame is made of steel, it is a Beretta model 70S.
If the frame is aluminum alloy, it is a Beretta model 71 Jaguar.
Both of these have been discontinued (at least as far as USA importation is concerned; they might still be available in other countries), and I'm not sure when they were first produced. It appears as though yours has a fixed rear sight, and along with the way the grips look, I'd say it was imported prior to the Gun Control Act of 1968, as after that law took effect many guns had to modified to meet the new import standards. Most smaller autoloading pistols had to have "target" grips and adjustable sights added to continue being imported.
Berettas are generally reliable and sturdy firearms, and after a quick checkup by a gunsmith, yours could probably be used for many more years. Finding magazines might be tricky, but Gun Parts Corp probably has some in stock.
The 70S models were fairly common in the late 80s/early 90s when I was getting interested in .22 pistols; I'd see them in shops and at gunshows pretty regularly. Not seen so much nowadays, but that just means that the folks that own them, like them and keep them.