Always remember: Considering single photon here: Rest mass of photon is zero. Relativistic mass of photon is finite but we will not take it into consideration. Relativistic Energy and Relativistic Linear Momentum of photon is not zero. read more
Photon carry Energy and Linear Momentum, though it has zero rest mass and finite relativistic mass. E ^2 = (p^2) c^2 + (m^2) c^4 This is the relativistic energy formula containing relativistic linear momentum and rest mass of photon. read more
"momentum is the product of mass and velocity, so, by this definition, massless photons cannot have momentum" This reasoning does not hold. Momentum is the product of energy and velocity. read more