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Using $p$-adic local Langlands correspondence for$\operatorname{GL}_2(\mathbb{Q}_p)$, we prove that the support of patchedmodules constructed by Caraiani, Emerton, Gee, Geraghty, Paskunas, and Shinmeet every irreducible component of the potentially semistable deformationring. This gives a new proof of the Breuil-M\'ezard conjecture for2-dimensional representations of the absolute Galois group of $\mathbb{Q}_p$when $p > 2$, which is new in the case $p = 3$ and $\bar{r}$ a twist of anextension of the trivial character by the mod p cyclotomic character. As aconsequence, a local restriction in the proof of Fontaine-Mazur conjecture byKisin is removed.

On the automorphy of 2-dimensional potentially semi-stable deformation rings of $G_{\mathbb{Q}_p}$