"Est-ce que je pourrais avoir l'un de ceci" won't do, whatever the case; "Est-ce que je pourrais avoir l'un de ceux-ci" is a possibility, although not usual, and the pronunciation is exactly the same. However, what you are asking for must be that type of thing available as units: buns, doughnuts, pastries, pieces of meat, whole fried chickens, chicken legs, etc. Nevertheless, it is more usual to use a generic term or the particular name; one possibility is using the name that's indicated near the piece of food you have in mind; otherwise you can ask the employee for the name, there is no problem.
You use more readily the pronoun "ceux-ci" when you choose certain pieces rather than others; that presupposes that you are able to make the difference, that you can see all that is being proposed, etc.
- — Je voudrais un blanc de poulet.
— Bien cuit, ou cuit à point ?
— Donnez-moi l'un de ceux-ci, bien cuit (s'il vous plait). _ or just as well: Donnez-m'en un bien cuit, (s'il vous plait) (without choosing). _ and simpler: Un bien cuit (s'il vous plait).
generic names: pâtisserie, pain, petit pain, dessert, plat, hors-d'œuvre, sandwich, …
If what you want is named by a mass noun, you can say "Est-ce que je pourrais avoir une portion de ceci ?". You can also use the word "plat" if what you want is a prepared dish.
- Je voudrais une (ou deux, trois, etc.) portions de ce plat. (*In almost all cases you have to point to the dish with your hand, but that goes without saying and is not particular to French I should say.)
- Est-ce que je pourrais avoir une (ou deux, trois, etc.) portion(s) de ce plat.
If the food has already been put onto dishes or into tubs you can say "Un de ces plats" and "une de ces barquettes (tub)"
You can say "Est-ce que je peux en avoir un ?" practically only when you first had a little talk with the employee so as to know better what you are going to buy or when you just asked for the name; in that case "Est-ce que je peux en avoir un ?" is perfect (remember the name of the thing must be countable, though).
"Est-ce que je pourrais un peu de cela/ceci" is not correct; "pouvoir", as in English, is always constructed with another verb.