Yes, the quarks that make up a neutron do have charges. Neutrons are composed of three quarks: two down quarks (with a charge of -1/3 each) and one up quark (with a charge of +2/3). The sum of the charges of these three quarks cancels out, resulting in a net charge of zero for the neutron.
Quarks are elementary particles that are considered to be the fundamental building blocks of matter. They come in six different flavors: up, down, charm, strange, top, and bottom. Each flavor of quark has a specific electric charge associated with it. The up quark has a charge of +2/3, while the down quark has a charge of -1/3. Other quarks have different charges, but the combination of these charges determines the overall charge of a composite particle like a neutron or proton.