There is no set time line for fellowship applications, but I think that if you know that you want to apply, you need to consider where you want to go and what type of focus (spine, sports, pain, SCI...). Once you have made this decision, I would suggest getting your CV, cover letter, and letters of rec ready for submission by the end of your third year.
Program directors like to make decisions by October or November of your senior year. In California, it may take 2-3 months to get a medical license and the interview period is too long to wait until feb or march. Most ACGME programs also interview medical students for residency positions. It is nice to get it over and done so the next year can be set. (Makes for a nice Christmas season).
To make a decision by a program, if the applicant has all the requiered documents in by May to July, an interview can be scheduled from July to October.
Not every program follows this time line, but it can't hurt to make an early jump. My experience is that I lost a position by the time September rolled around.