Professor refuses to write a recommendation letter to students who haven't written a research paper with him
I wanted to ask whether his refusal for recommendation letters is reasonable 


My personal opinion is that if you worked in his lab for a year (satisfactorily), it is unreasonable to refuse a letter. All the more so if you had other good interactions (TAing, etc.) with him.


  and also ask for some advice on how to handle this situation!


Unfortunately, my opinion counts for absolutely nothing. You cannot force this professor to write you a letter, and would be unwise to try. All you can do is find someone else. Preferably someone who can comment on your research, or at least someone who can confirm that your advisor almost never writes letters for undergrads (i.e., vouching that the lack of a letter from your advisor should not reflect poorly on you).