Trying to lose fat while not losing strength sucks. You feel weak when you lift, you're hungry during the day, and all of those strength gains you worked for slowly, but surely bleed out of you. If you do it wrong, you come out of the cut at the same weight and strength as before you started your strength training. If you do it right, you'll lose a little bit of strength, but a lot of fat. The best way, in terms of nutrition, to cut fat while maintaining strength is to eat foods high in protein. However, it can be difficult to get the necessary protein when on a caloric deficit, so you need to buy foods that have a high protein to calorie ratio.
Conversely, if you're trying to lose fat and don't care about strength losses, you'll find high protein foods to be helpful. Protein is extremely filling; I can crush a dozen donuts totaling 4,000 calories in one sitting, but I can barely finish a pound of chicken totaling 700 calories.
Get ready to consume chicken breast after chicken breast after chicken breast, because it's almost entirely protein and it's cheap. Fat trimmed chicken is about 96% protein by calories. Learn how to grill, cook, and bake this stuff, because you will eat a lot of it.
Now Foods 100% Protein Isolate
Protein isolate is not actually 100% protein; it has some sugar in it (~1g per scoop). By calories, it's 91% protein, so it's quite high in protein. Buy the unflavored stuff and use a mixer to mix it with diet soda. It doesn't taste amazing, but it's a pretty easy way to start the morning with lots of protein.
Tilapia and Canned Light Tuna
When you get sick of chicken, it's time to switch to fish. Tilapia is 84% protein by calories and is pretty bland, so whatever you spice it with will dominate the taste. Lemons or thyme or lemon pepper taste fine and aren't too potent.
Canned tuna (89% protein) has a more distinct taste and is cheap. It's easy to prepare and can be mixed with spices to make a good sandwich. PRO TIP: toast one side of the bread and make that the bottom so that the top piece of bread doesn't squeeze the tuna out of the perimeter or cut the roof of your mouth.
Egg whites have 78% protein, but damnit, I can't bring myself to waste that delicious yolk. If you find yourself desperate enough or legitimately like them, egg whites can be a great way to start the morning.
You will have to find a way to get enough protein while on a cut, and these five foods can help. Try them all, and you'll at least find a few that work well for you. Most importantly, if your fat loss is not going well, figure out why and don't give up.