If you do decide to enter a paid contest, make sure its sponsor is worth putting on your resume. (Joe Blow's novel of the year contest will do nothing for your career.)
You can find some paid contests here:
DIY: Book Awards For Self-Published Authors
10 Awards for Self-Published Books
The Book Designer Monthly Ebook Cover Design Awards
Joel Friedlander's self-publishing site is heavily trafficked, so this contest is well worth entering. There is no restriction on publication date, but the e-books must be published at the time of submission. If you don't yet have a cover for your book, looking at previous winners is great inspiration.
Historical Novel Society Indie Award
HNS Indie Award, first offered in 2014, recognizes excellence in indie-published historical novels. Restrictions: English language only. Prize: The winner shall receive £100 or $100 ($100Aus). How to enter: Click HERE for complete rules.
You Write On
"For an opportunity to be eligible for the YouWriteOn Book of the Year Awards, simply join YouWriteOn.com at any time for free and upload your opening chapters or short stories. Each month the highest rated books receive feedback from editors for leading publishers, such as Random House and Orion, whose authors include Dan Brown, John Grisham, Bill Bryson and Ian Rankin. These stories enter the YouWriteOn BestSellers Chart and are then eligible for our Book of the Year Awards in the next year."