Prerequisites for studying parametrized complexity
This shouldn't come as a surprise, but you should definitely be familiar with algorithms and datastructures as well as complexity theory.
Two fundamental text books are downloadable for free, and you can probably find the answer to your question there:

Marek Cygan, Fedor V. Fomin, Lukasz Kowalik, Daniel Lokshtanov, Daniel Marx, Marcin Pilipczuk, Michal Pilipczuk, and Saket Saurabh, Parameterized Algorithms, Springer, 2015
Fedor V. Fomin, Daniel Lokshtanov, Saket Saurabh, and Meirav Zehavi, Kernelization. Theory of Parameterized Preprocessing, Cambridge University Press, 2019.


But to give my own short answer:
I think knowing some recursion theory (computation theory) is of benefit, since some of the levels in the parameterized hierarchies are based directly on Turing machine theory.
Most crucial is it that you have a good understanding of the complexity classes P and NP, and how to prove that algorithms are running in polynomial time, and how to prove that some problems are NP-complete.
Parameterized complexity is a fun area, enjoy your journey!