Is it permissible for us to gather to study knowledge in our country where that is forbidden except with a permit, and what should we do if the permit request is denied?

If the decision to prohibit gatherings applies only to mosques, and Muslims fear harm to themselves or their families, then they should not gather in the mosque. Rather, they can acquire knowledge by gathering in one of their homes, or in any private place. If gathering is not possible, there are many means of seeking knowledge that do not bring harm.