The phrase 'a tiny portion of' is correct and usable in written English.
You can use this phrase to describe a small amount of something. For example, "I only had a tiny portion of cake at the party."
A tiny portion of roast beef.
It amounts to a tiny portion of the federal budget.
(A tiny portion of the collection is currently available digitally).
Even with access, it is possible to reach only a tiny portion of the Chinese.
The procedure worked properly in only a tiny portion of those tested.
And yet spending on cycling in London is still a tiny portion of the transport budget.
But those cases make up a tiny portion of the total juvenile caseload nationwide.
Hydroelectric stations and other power sources constitute only a tiny portion of the total.
They sit right below the Supreme Court, which accepts only a tiny portion of appeals.
A tiny portion of noodles with spicy squid vanished without impact.
Fortunately, they got their hands on only a tiny portion of the library's collection.
