Wide range Ohmic region Mosfet
I can only give you a link to Digi-Key where you can search for any MOSFET you like.
I have already pre-selected only active, in-stock, N-channel, Vgs threshold at 5V@250μA, through hole MOSFETS for you. Just remember that it is better to use a MOSFET with a higher current rating if you expect to be using it at its maximum.
You just have to select the one you like:
https://www.digikey.com/products/en/discrete-semiconductor-products/transistors-fets-mosfets-single/278?k=&amp;pkeyword=&amp;sv=0&amp;sf=1&amp;FV=69%7C411897%2C606%7C378999%2C1989%7C0%2C-8%7C278%2C1236%7C249240&amp;quantity=&amp;ColumnSort=0&amp;page=1&amp;stock=1&amp;pageSize=500  

EDIT: Most MOSFETs can be used as variable resistors but in a very limited Vgs and Vds area. You need to use the ohmic region between zero Vgs and their rated turn on Vgs (Vgs threshold).
After searching a little more, I have come across LINEAR series MOSFETs on Digi-Key. They have a wider ohmic region than the ordinary MOSFETs, but are not cheap.
https://www.digikey.com/products/en/discrete-semiconductor-products/transistors-fets-mosfets-single/278?k=linear+mosfet&amp;k=&amp;pkeyword=linear+mosfet&amp;sv=0&amp;pv69=411897&amp;sf=1&amp;FV=-8%7C278&amp;quantity=&amp;ColumnSort=1000011&amp;page=1&amp;pageSize=500  

P.S.: In 1999., my supervisor (an electrical engineer) tasked me with making an adjustable load using a MOSFET, a potentiometer and a 9V battery. He gave me the simple schematic, and if I remember correctly, the circuit worked. We needed simple and cheap DC loads for testing DC-DC converters made with our company's ICs, as the commercial variable loads were expensive (we had programmable electronic loads by HP). The load voltages were mainly up to 5V, so this was doable with a MOSFET. I don't remember which MOSFET model did we use.