Original:

The mob flowed around Barc.

His bare feet stood firm on the muddy ground, despite the mass of people shouldering its way through, urging him to move on. Close to fifty men, their faces glistening through the rainy night and torch lights flickering in their zealous eyes, they had been searching for the heretic in the narrow streets of the lower city for the last hour. Barc had been walking with them until seconds ago. Until he had sensed the hunt nearby.

One of them mumbled something as he passed along with a disapproving stare. Barc closed his eyes. He breathed in the fresh smell of earth. _Focus now_.

“Follow your hearts whenever you feel lost in the sacred path of the sun god, brothers!” shouted a high-pitched voice from the front

Revised:

The mob flowed around Barc.

His bare feet stood firm on the muddy ground, despite the mass of people, close to fifty men, shouldering past him, urging him to move on. Their faces glistened through the rainy night and torch lights flickered in their zealous eyes. Barc had been a part of the mob until seconds ago, hunting the heretic in the narrow streets of the lower city, making sure they didn't reach the man before he did.

One of them mumbled something as he passed along with a disapproving stare. Barc closed his eyes. He breathed in the fresh smell of rain in the air. Focus now.

“Brothers! Follow your hearts!” shouted a high-pitched voice from the front. “The sun god will guide you whenever you feel

Revised 2:

The mob flowed around Barc. His bare feet stood firm on the muddy ground, despite the mass of people, close to fifty men, shouldering past him, urging him to move on. Barc had been dragging himself along with them for the good part of an hour now, hunting the heretic in the narrow streets of the lower city.

The heretic. What irony it was. If this mindless swarm was so keen on purging twisted beliefs then all they needed to do was build a pyre and cast themselves into the embrace of their misbegotten god. Oh, my beloved prophet, help me.
Thankfully Barc did not need to put up with their filthy faces glistening through the rainy night anymore. The first part of his task, making sure they didn't reach the man before he did, was just about to be done.

It’s interesting that he made this significant shift in his focus and actions, but it needs to be tweaked. First he was with the group, searching for the heretic. Then he stopped because he sensed the hunt nearby. But isn’t he a part of the hunt? How could it be nearby when he is a part of it? (I suspect you mean some other hunt, but that isn’t clear.) This is my #1 comment.

“mass of people shouldering its way through” sounds like going through a doorway or other space, but before and after you talk about Barc. I think it would be better to say they shouldered past [him].

Sentence structure is off: Close to fifty men, their faces glistening, they had been … “they” is extra.
I’d almost want to split it, with the first sentence as a fragment: Close to fifty men, their faces glistening … eyes. They had been…

“Barc had been walking with them until seconds ago.“ just walking? Seems like a stronger verb could be used here, some indication of his involvement. Was he just along for the ride or had he been in the throes of zealousness?
I suspect I would rather see the before and after, with the shift as it happens, especially since it just happened seconds ago. This is my #2 comment.

They are in a city, but he smells the fresh scent of earth? That sounds like farmland, not a city street. If you mean he smells something from a different place, that needs to be stated.

_Focus now_. To do italics, put [] at the start and end of the fragment, with i inside the first set and /i inside the second set (try to edit my post to see how I did it). Like this: Focus now.

despite the mass of people shouldering past him, urging him to move on. Close to fifty men. First you say "mass of people" and then immediately quantify it as "close to fifty men" Why not save yourself a couple of words and just say something like "Barc stood firm on the muddy ground, close to fifty men shouldering past him."?

Does a face really glisten "through" the night? Sounds weird to me. Maybe "glistening in the rain"?

In many ways, your hook is the biggest flaw in this opening for me. "Sensed" is such a weak word and doesn't really tell the reader an awful lot. In what way does he sense the hunted? And I also can't help wondering why Barc is part of a mob and when he finds his quarry he suddenly stops dead...I'm in two minds about that--whether it's a decent hook in itself, or you're missing the chance of a stronger hook by giving the reader a little hint about why the sudden change in Barc's behaviour.

I suspect withholding. We should know what your MC knows, and something of what he feels/cares about.

Yes to combining “mass of people" and "close to fifty men”. Also I notice lots of repetition of him standing still and others going by. I’d suggest, loose your first sentence and start with “Barc’s bare feet…”

I think “before he does” should be “before he did” (for correctness). “first” or “before him” might be better.

“Barc had been a part of the mob until seconds ago, hunting the heretic in the narrow streets of the lower city, making sure they didn't reach the man before he does.” The transition doesn’t work as its worded, because it sounds like he wasn’t really “part of” the mob to begin with, if he had/has a separate agenda.

His motivation is still unclear; does he want to catch the heretic to rescue him, kill, him, what? (I can wait on the motivation if it comes soon, BUT right now I don’t know anything about Barc; is he the good guy? Should I like him?)

Here is a lame suggestion: Barc had given up on trying to get ahead of this mob. He couldn’t let the heretic fall into their cruel hands! The fool might be anywhere, hiding in the city’s narrow streets. Barc would have to use his super-special powers to search out the fugitive. (I really don’t like the “had” tense, or the three separate nouns for the heretic; and hiding in the streets doesn’t make sense. But the idea is to give us more of Barc’s thoughts.)

However, because the second paragraph is far more dominated by the POV than the first, they feel disconected. This hampers the hook of why Barc is hunting for the heretic with the mob. Blending the paragraphs in terms of tone and prevelance of the POV as well as more clearly defyning how at odds Barc is with the mob may help with the hook. Though leaving Barc's full intentions vague may be a concious decision on your part and effect the story, if so feel free to ignore that part of the comment.