What are the various ways of reciting the Basmala between the middle of the surahs, and what is the reference for that?

Seeking refuge (Audhubillah) is required when starting from the middle of a surah, and it is permissible to follow it with the Basmalah (Bismillah). However, when transitioning between surahs, there are four permissible ways: cutting off all (ending the surah, then Basmalah, then starting the new surah), cutting off the first (ending the surah) and connecting the second (Basmalah) to the third (starting the new surah), and connecting all (ending the surah and connecting it to the Basmalah, which is then connected to the beginning of the new surah). As for connecting the end of a surah with the Basmalah and stopping there, this is a forbidden way because the Basmalah is for the beginnings of surahs, not their endings. Also, the Basmalah is not required when transitioning from a surah to the middle of another surah.