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We explore the first radial excitation $X_{\mathrm{4c}}^{\ast}$ of the fullycharmed diquark-antidiquark state $X_{\mathrm{4c}}=cc\overline{c}\overline{c} $built of axial-vector components, and the hadronic molecule $\mathcal{M}=\chi_{c1}\chi_{c1}$. The masses and current couplings of these scalar statesare calculated in the context of the QCD two-point sum rule approach. The fullwidths of $X_{\mathrm{4c}}^{\ast}$ and $\mathcal{M}$ are evaluated by takinginto account their kinematically allowed decay channels. We find partial widthsof these processes using the strong couplings $g_i^{\ast}$ and $G_i^{(\ast)}$at the $X_{\mathrm{4c}}^{\ast}$($\mathcal{M}$ )-conventional mesons verticescomputed by means of the QCD three-point sum rule method. The predictionsobtained for the parameters $m=(7235 \pm 75)~ \mathrm{MeV}$, $\Gamma=(144 \pm18)~\mathrm{MeV}$ and $\widetilde{m}=(7180 \pm 120)~\mathrm{MeV}$,$\widetilde{\Gamma}=(169 \pm 21)~\mathrm{MeV}$ of these structures, arecompared with the experimental data of the CMS and ATLAS Collaborations. Inaccordance to these results, within existing errors of measurements anduncertainties of the theoretical calculations, both the excited tetraquark andhadronic molecule may be considered as candidates to the resonance $X(7300)$.Detailed analysis, however, demonstrates that the preferable model for$X(7300)$ is an admixture of the molecule $\mathcal{M}$ and sizeable part of$X_{\mathrm{4c}}^{\ast}$.

Resonance $X(7300)$: excited $2S$ tetraquark or hadronic molecule $\chi_{c1}\chi_{c1}$?