Requesting a favor from student for giving recommendation letters Can I ask/ insist a bright undergraduate student (who is having similar areas of interest) to work under me for his final year project period and try to come up with a scientific publication in favor for giving him recommendation letters for internships?
It sounds like what you want to do is to write a letter now in exchange for the promise that they will work for you later. Whether you can do this is down to your university's rules, but I would argue that it is unethical and unwise to coerce a student in this way. 

My recommendation would be to accede to the request and make the offer


  Sure, I can write you a strong letter. For that matter, if you are looking for research experience, I would be happy to supervise your senior project next year. Let's chat sometime if you are interested.


If you are not willing to write the letter:


  My policy is to only write recommendation letters for students who do research with me. That said, I'd be happy to discuss hiring you as a research assistant next year.


Note, this second one still links the two, but it simply tells the student your requirements, rather than suggesting quid pro quo.