But whoever speaks against the Holy Spirit will not be forgiven in this world or the next. Jesus
This statement demonstrates, without doubt, the possibility of the forgiveness of some sins in the next world.
The passage from Corinthians fleshes out this process a bit more.
I don't know what translation you are using, but here are three quotes referencing what you are speaking of:
"Whoever speaks a word against the Son of Man will be forgiven, but whoever speaks against the Holy Spirit will not be forgiven, either in this age or in the age to come." [Mt. 12:32]No one who commits this grievous sin will enter heaven.
"But whoever blasphemes against the Holy Spirit can never have forgiveness, but is guilty of an eternal sin." [Mk. 3:29]
"And everyone who speaks a word against the Son of Man will be forgiven; but whoever blasphemes against the Holy Spirit will not be forgiven." [Lk. 12:10]
And it WILL not be purged it the un-Biblical purgatory of Catholicism.