Triple heavy flavour baryons are studied using the hypercentral description of the three-body system. The confinement potential is assumed as hypercentral Coulomb plus power potential with power index 𝑝. The ground state ($J^{P} = \dfrac{1}{2}^{+}$ and $\dfrac{3}{2}^{+}$) masses of heavy flavour baryons are computed for different power index, 𝑝 starting from 0.5 to 2.0. The predicted masses are found to attain a saturated value with respect to variation in p beyond the power index $p$ > 1.0. Using the spin-flavour structure of the constituting quarks and by defining effective mass of the confined quarks within the baryons, the magnetic moments are computed with no additional free parameters.