A millisecond pulsar having an ellipticity, that is an asymmetric mass distribution around its spin-axis, could emit continuous gravitational waves, which have not been detected so far. An indirect way to infer such waves is to estimate the contribution of the waves to the spin-down rate of the pulsar. The transitional pulsar PSR J1023+0038 is ideal and unique for this purpose, because this is the only millisecond pulsar for which the spin-down rate has been measured in both accreting and non-accreting states. Here we infer, from our formalism based on the complete torque budget equations and the pulsar magnetospheric origin of observed $gamma$-rays in the two states, that PSR J1023+0038 should emit gravitational waves due to a permanent ellipticity of the pulsar. The formalism also explains some other main observational aspects of this source in a self-consistent way. As an example, our formalism naturally infers the accretion disc penetration into the pulsar magnetosphere, and explains the observed X-ray pulsations in the accreting state using the standard and well-accepted scenario. This, in turn, infers the larger pulsar spin-down power in the accreting state, which, in our formalism, explains the observed larger $gamma$-ray emission in this state. Exploring wide ranges of parameter values of PSR J1023+0038, and not assuming an additional source of stellar ellipticity in the accreting state, we find the misaligned mass quadrupole moment of the pulsar in the range of $(0.92-1.88)times10^{36}$ g cm$^2$, implying an ellipticity range of $(0.48-0.93)times10^{-9}$.
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