  We proposed five $f(Q,T)$ models, which are an extension of symmetric
teleparallel gravity, where $Q$ is the non-metricity and $T$ is the trace of
the stress-energy tensor. By taking specific values of their parameters, these
models have a $\Lambda$CDM limit.
  Using cosmic chronometers and supernovae Ia data, we found that our models
are consistent with $\Lambda$CDM at a 95\% confidence level. To see whether one
of these models can challenge $\Lambda$CDM at a background perspective, we
computed the Bayesian evidence for them and $\Lambda$CDM. According to it, the
concordance model is preferred over four of them, showing a weak preference
against $f(Q,T) = -Q/G_N + bT$ and $f(Q,T) = -(Q+2\Lambda)/G_N +bT$, a
substantial preference against $f(Q,T) = -(Q+2 H_0^2 c (Q/(6H_0^2))^{n+1})/G_N
+ bT $, and a strong preference against $f(Q,T) = -(Q+2H_0^2c(Q/(6H_0^2))^{n+1}
+ 2\Lambda)/G_N + bT$. Interestingly, a model includying a $T^2$ dependence
($f(Q,T) = -(Q+2\Lambda)/G_N - ((16\pi)^2 G_N b)/(120 H_0^2) T^2$) showed a
{substantial} preference against $\Lambda$CDM. {Therefore, we encourage further
analyses of this model to test its viability outside the background
perspective.}
