Does the skin taste sweet, and the flesh lemon sour? If so, I think it's calamondin (aka calamansi). If it's sweeter than that, I'd guess some sort of mandarin like you were thinking. There appear to be multiple varieties of mandarin oranges (satsumas, tangerines, and clementines are all considered mandarins). Lucky you to have such a productive tree!

Calamansi? I recall having them decades ago in Southeast Asia.