I'm going to recommend you (or anyone else interested in this topic) read Stalin: The Court of the Red Tsar by Simon Sebag Montefiore.

The word "remorse" does not appear in that book.

However, "sorrow" does show up on page 525 of the 2007 edition:

"Yet Stalin talked about their acquaintances murdered during the thirties 'with the calm detachment of a historian, showing neither sorrow nor rage, just a light humour.' Once he wandered up to one of his marshals who had been arrested and released: 'I heard you were recently in confinement?'

'Yes, Comrade Stalin, I was, but they figured out my case and released me. But how many good and remarkable people perished there.'

'Yes,' mused Stalin thoughtfully, 'we've lost a lot of good and remarkable people.' Then he walked out of the room into the garden. The courtiers turned on the Marshal. 'What did you say to Comrade Stalin?' demanded Malenkov who always behaved like the school prefect. 'Why?' Then Stalin reappeared holding a bouquet of roses which he presented to the Marshal as a weird sort of apology."

You ask about Yakov in particular, and that's referenced in the first two pages of the 40th chapter:

"After the war, a Georgian confidant plucked up the courage to ask Stalin if the Paulus offer was a myth.

"He 'hung his head,' answering 'in a sad, piercing voice': 'Not a myth ... just think how many sons ended in camps! Who would swap them for Paulus? Were they worse than Yakov? I had to refuse ... what would they have said of me, our millions of Party fathers, if having forgotten about them, I had agreed to swapping Yakov? No, I had no right ...' Then he again showed the struggle between the nervy, angry, tormented man within and the persona he had become: 'Otherwise I'd no longer be "Stalin."' He added: 'I so pitied Yasha!'"