Check out the Codex on Upgrading Across Multiple versions.
Regarding the upgrading steps, it says:
If you plan on upgrading across more than two major releases, please
consider upgrading incrementally to avoid potential conflicts and
minimize the risks of database damage. For example, if you plan on
upgrading from 2.5 to 4.1.1, upgrade to 2.7 first, followed by 2.9,
then 3.1, and so on. Essentially, it’s okay to skip one release, but
never skip TWO when upgrading.
So according to this advice, your upgrade sequence could be:
3.5.1 -> 3.7.x -> 3.9.x -> 4.1.1
I agree with the comments by @Milo and @PieterGoosen; You shouldn’t experiment with this on a production install, test this first on your dev install. Deactivate plugins before the upgrades and activate them afterwards, one at a time. Remember to activate the debug log and scan through the debug.log for errors.
Remember to backup everything.
You can find the old releases here.