Each month the Masters Review* summarizes contests and prizes with deadlines in that month on their website. The majority of the contests they list have low entry fees. Some are free.
For a look at contests with submission deadlines in January, check out this link.
The Masters Review own Winter Short Story Contest submission deadline is also in January, on January 31. For details on the contest and the prizes offered, see their website here. Only emerging writers are eligible to enter. Winners and runners-up receive agent reviews.
*(from The Masters Review website): Always a free way to submit. Always paid for your work. The Masters Review offers a quality platform for emerging writers.
Founded by Kim Winternheimer in 2011, the Masters Review is an online and in print publication celebrating new and emerging writers. We are on the lookout for the best new talent with hopes of publishing stories from writers who will continue to produce great work. We offer critical essays, book reviews by debut authors, contest deadlines, submissions info, and interviews with established authors, all with the hopes of bridging the gap between new and established writers.