You might be interested in this previous answer I wrote on the subject.

I lay out the reasons in that thread why I'm skeptical. I think it's important to note that Russia was not at peace at the time of the bombings: there was an insurgency underway in Dagestan that was being assisted by the Chechen Shamil Basayev and his group, as well as the Saudi Ibn al-Khattab. While the two apartment building explosions in Moscow were the most deadly, they tend to get melded with the Ryazan Apartment Building incident, which is either considered a "smoking gun" for a false flag operation or a botched FSB drill. Either way, these three incidents took place in a Russia that had already been experiencing other, smaller bombing incidents for weeks, and as far as I can tell no one has ever claimed that those bombing incidents (mostly car bombs) were not the work of militant groups. The other big issue is that most of the people who have claimed that it was all an FSB operation have usually been political opponents (mostly in exile) of Putin, and they have had their own motivations for making these claims. Usually their specific statements consider the theory "credible" but haven't provided specific evidence to back it up.

The honest answer is that probably we won't ever actually know. Whether as part of an intentional coverup or not, a lot of the evidence connected with the Moscow apartment bombings was destroyed by investigators not long after the incidents.