Yes, quarks do have mass, although their masses are relatively small compared to the masses of composite particles, such as protons and neutrons, in which they are found.
There are six known types, or flavors, of quarks: up (u), down (d), charm (c), strange (s), top (t), and bottom (b). The up and down quarks are the lightest, with masses on the order of a few MeV/c^2 (megaelectronvolts divided by the speed of light squared). The masses of the other quarks increase significantly, with the top quark being the heaviest, with a mass of about 173 GeV/c^2 (gigaelectronvolts divided by the speed of light squared).
The masses of quarks are not directly measured as individual quantities but are determined through their effects on the behavior of particles and the dynamics of the strong nuclear force, which governs their interactions. The masses of quarks also play a role in determining the masses and properties of composite particles, such as hadrons (protons, neutrons, etc.), which are bound states of quarks.
It's worth noting that the masses of quarks are not static values but can be influenced by their interactions with the Higgs field, a quantum field associated with the Higgs boson. The Higgs field gives rise to the phenomenon of mass generation in the Standard Model of particle physics, which is the current theoretical framework describing elementary particles and their interactions.
In summary, quarks do possess mass, although the masses of different quark flavors vary, with the up and down quarks being the lightest and the top quark being the heaviest. Quark masses play a significant role in determining the properties and behavior of particles and the strong nuclear force.