  Strong evidence of the existence of the Stochastic Gravitational-Wave
Background (SGWB) has been reported by the NANOGrav, PPTA, EPTA and CPTA
collaborations. The Bayesian posteriors of the Gravitational-Wave Background
(GWB) amplitude and spectrum are compatible with current astrophysical
predictions for the GWB from the population of supermassive black hole binaries
(SMBHBs). In this paper, we discuss the corrections arising from the extra
scalar or vector radiation to the characteristic dimensionless strain in PTA
experiments and explore the possibility to detect charges surrounding massive
black holes, which could give rise to SGWB with vector or scalar polarizations.
The parametrized frequency-dependent characteristic dimensionless strain is
used to take a Bayesian analysis and the Bayes factor is also computed for
charged and neutral SMBHBs. The Bayesian posterior of GWB tensor amplitude is
$\log_{10} A_T=-14.85^{+0.26}_{-0.38}$ and spectral exponent
$\alpha=-0.60^{+0.32}_{-0.36}$. The Bayesian posterior for vector or scalar
amplitude $A_{V, S}$ is nearly flat and there is nearly no constraint from the
current observation data. The Bayesian factor is $0.71$ far less than 100, so
the current observation can not support the existence of the charged SMBHB.
