A Priest is Not His Own by Sheen
30 Questions on Celibacy (not a novel, but still good reading), various authors, published by Ignatius
The Seven-Storey Mountain by Merton
Life of Christ by Sheen
Insofar as fiction written about the process of discernment, I’m not sure there are any. If there were, they’d have a limited readership at best, I would think (I have a vocation, but don’t really read fictional stuff). Not to mention the countless problems such novels would likely have with orthodoxy and Church doctrine, as many, many, Catholic books - even with the imprimatur - do. It would be a prime target for heterodoxy and the Modernist heresy.
I think the best bet for something in the same ball-park as you want, is reading the memoirs of priests, or priests’ retelling of their own discernment, or the same but of religious brothers, and similar materials.