Hello,
Since I migrated my site from version 3.x (yes I've come a long way ) to 8.1.2, I've noticed several redirects (see attachment) to the same url only on the search page (/index.php?page=search&sCategory=117).

Have you already encountered this problem?

Thanks in advance

I would say you have some invalid info in config.php

I don't know what I've done wrong in config.php.

That looks fine, usually relative path is wroong.
Maybe its jist your localhost

Actually /mysite/ might go to relative url

I'm using mamp on my computer. So, if I remove /mysite/ I've homepage of my server. That's seems normal

The issue is located in this file osclass-v8.1.2/oc-includes/osclass/controller/search.php arround line 224.
In fact, after first load $searchUri == $_base_url . $this->uri then we loop on same url ($this->redirectTo($searchUri, 301)).

When I comment this block, my website seems work.

Well its there for a reason. Issue will be on your side, pretty sure about that.

I think but I'm struggling with issue. The only fix that I've today is to comment this section

Its trying to use "better" url but condition is never satisfied.
Keep note and when you move to server you may try to enable.