  We present a more general form of the Schr\"odinger equation in curvilinear
space that is exposed to external fields. Thereby, we solve the wave equation
with the Cornell plus harmonic potentials (CHP) under the influence of the
magnetic and Aharonov-Bohm (AB) flux fields using curvilinear coordinates
system in such space. With this requirement, the energy spectrum and the
corresponding wave functions are calculated by means of the series method. The
mass spectrum of both charmonium and bottomonium states consisting of quark and
antiquark are calculated. In addition, the main thermodynamic functions such as
the free energy, the mean energy, the entropy, the specific heat, the
persistent currents and magnetization are obtained by using the characteristic
function. We draw the resulting energy states and the thermodynamic quantities
versus some potential parameters, magnetic field and temperature to see their
numerical behaviors. Finally, we give some discussions to our results.
