If I miss repeating the Adhan from the beginning, should I repeat what I missed, or should I continue from where the muezzin has reached?

If you hear part of the adhan and miss its beginning, then say only what you heard, because the Prophet, peace and blessings be upon him, said: "When you hear the muezzin, then say as he says." If you hear the beginning of the adhan but miss following some of it, then start from its beginning and make up what you missed, then complete the rest with the muezzin. The catching up of the following should be done soon, not after a long separation.