Fantasy or Grimdark Fantasy. Main character rides a lizard and his own father and son. Read 2000-2018.

[Sam]

When I read it - somewhere between 2000 and 2018,
Language of that book is English
What I remember - it's a fantasy, maybe grimdark, solo book or the first one in the series.
The plot is: there was a man who patrolled a magical desert and rode a fancy riding lizard. And he got stuck in a time loop, but somehow possessed his unborn son. The main protagonist is that son who also patrolling that desert and got to a specific place and remembered that he is his father the whole time.

What I do not remember - the author or the title, I searched high and low and in Chatgpt, which did not help at all.
Thanks in advance