Generally, no, you shouldn't cover the pan when shallow-frying chicken patties, as doing so can steam them and prevent them from getting that lovely crispy outside.
When you cover your pan during shallow frying, you're essentially trapping steam. This steam then condenses back into water, which drips onto your food. This creates a moist environment that stops that crispy crust from forming, leaving you with a soggy or less-than-perfectly-browned exterior. While covering might help thicker items cook faster internally, for chicken patties, the whole point of shallow frying is to get that delicious, crispy outer layer. It's much better to rely on medium-high heat and the right cooking time to cook your patties all the way through. If you notice your patties browning too quickly on the outside but still seem undercooked inside, try lowering the heat a bit and cooking them for a longer time, rather than covering them.
For thicker chicken patties, after you've browned them beautifully in the pan, you can pop them into a preheated oven for a few minutes to ensure they cook through completely without over-browning the outside.