A congruence involving alternating harmonic sums modulo $p^{\alpha }{q}^{\beta }$

In 2014, Wang and Cai established the following harmonic congruence for any odd prime $p$ and positive integer $r$, \begin{equation*} \sum\limits_{i+j+k=p^{r}\atop{i,j,k\in $\mathcal{P}${p}}}\frac{1}{ijk}\equiv-2p^{r-1}B{p-3} ~(\bmod ~ p^{r}), \end{equation*} where ${\mathcal{P}}_n$ denote the set of positive integers which are prime to $n$. In this note, we obtain the congruences for distinct odd primes $p,q$ and positive integers $\alpha ,\beta$, \begin{equation*} \sum\limits_{i+j+k=p^{\alpha}q^{\beta}\atop{i,j,k\in$\mathcal{P}${pq}\atop{i\equiv j\equiv k\equiv 1\pmod{2}}}}\frac{1}{ijk}\equiv\frac{7}{8}(2-q)(1-\frac{1}{q^{3}})p^{\alpha-1}q^{\beta-1}B{p-3}\pmod{p^{\alpha}} \end{equation*} and \begin{equation*} \sum\limits_{i+j+k=p^{\alpha}q^{\beta}\atop{i,j,k\in $\mathcal{P}${pq}}}\frac{(-1)^{i}}{ijk} \equiv \frac{1}{2}(q-2)(1-\frac{1}{q^{3}})p^{\alpha-1}q^{\beta-1}B{p-3}\pmod{p^{\alpha}}. \end{equation*} Finally, we raise a conjecture that for $n>1$ and odd prime power $p^{\alpha }\mathrm{\mid }\mathrm{\mid }n$, $\alpha \ge 1$, \begin{eqnarray} \nonumber \sum\limits_{i+j+k=n\atop{i,j,k\in$\mathcal{P}${n}}}\frac{(-1)^{i}}{ijk} \equiv \prod\limits{q|n\atop{q\neq p}}(1-\frac{2}{q})(1-\frac{1}{q^{3}})\frac{n}{2p}B_{p-3}\pmod{p^{\alpha}} \end{eqnarray} and \begin{eqnarray} \nonumber \sum\limits_{i+j+k=n\atop{i,j,k\in$\mathcal{P}${n}\atop{i\equiv j\equiv k\equiv 1\pmod{2}}}}\frac{1}{ijk} \equiv \prod\limits{q|n\atop{q\neq p}}(1-\frac{2}{q})(1-\frac{1}{q^{3}})(-\frac{7n}{8p})B_{p-3}\pmod{p^{\alpha}}. \end{eqnarray}