quodsi is a conj. meaning "but if", with "adversary force". Does it lead a conditional clause or a concession one? What does "but if" mean actually? Thanks.
Quodsi is just one example of how quod can precede a conjunction. It is simply a convention to spell it as one word if the conjunction is si, but not in other cases, and a convention, I believe, disparaged by many (including certain dictionaries). Similarly, you can occasionally read quod nisi, quod ne, quod utinam, quod cum etc. (for a long list of examples, see Forcellini: Quod ¶ 9).
This usually happens at the start of a sentence and serves to connect it to the previous one. It has an “adversary force” in the sense that it signals that the new thought which will now follow is somehow opposed to the one expressed immediately before, provides a counterpoint to it, puts it in perspective, or such. It is similar to sed or autem. So instead of si autem Romam veniam you could also write quod si Romam veniam.
Like but in English, the adversary force is often weak and seems more to keep the train of thought going. In fact, I'd say that "but if" is almost always bound to be a mistranslation for quodsi, and something like "now if," or simply "if," is better suited.
Also note that when you encounter quod followed by a conjunction, it is also possible (and probably far more likely) that it is a relative pronoun (quod si fieret etc.), which then has nothing to do with all these considerations.