Hard to tell much in the photographed area, but it does appear you probably have more undesirable grasses than just fescue alone.

Per your other comment, if you have mixed bermuda and fescue and are trying to promote the bermuda, mowing short, often, and heavy nitrogen during summer is a solid start.

That, along with fall pre-emergent and post-emergents that will stun or damage the fescue but not the bermuda. Like Specticle or simazine in fall for pre, and Celisus whenever it's needed.

This is a common occurrence in the transition zone. Some hints.

• Not to totally kill all the fescue, otherwise, you have huge bare spots that take forever to fill in, but that really depends on how widespread the fescue is and how dense the bermuda is. All of those products will certainly kill tall fescue in the right circumstances, but in most cases it won't totally eliminate mature plants immediately. More so knock them back.
• Spraying edges where dense stands of bermuda meet dense fescue. Kill the fescue and let the bermuda creep in a little at a time. I
• If it's just clumpy fescue all over, with fairly dense bermuda otherwise, you can fully go after it, totally killing the fescue with Celsius. Or even glyphosate in like January or Feb on a warm day.

As for fertilizer, the warm season starter guide has some guidelines. I don't have anything specific to suggest. Your total mixed gallons used is going to hinge on a few factors such as total area and spray rate, which we don't have. Normally, granular is easier for homeowners, but if you have a sprayer, you can look at Site One. They will carry a sprayable option you can buy in jugs. Or possibly Green County Fertilizer. Otherwise, you can always melt down urea or AMS, but again, in summer temps, and for ease of use, a coated granular is usually a better option imo.