We provide the indication of high flux of $^{40}$K geo-antineutrino and geo-neutrino ($^{40}$K-geo-($\bar{\nu} + \nu$)) with Borexino Phase III data. This result was obtained by introducing a new source of single events, namely $^{40}$K-geo-($\bar{\nu} + \nu$) scattering on electrons, in multivariate fit analysis of Borexino Phase III data. Simultaneously we obtained the count rates of events from $^7$Be, $pep$ and CNO solar neutrinos. These count rates are consistent with the prediction of the Low metallicity Sun model SSM B16-AGSS09. MC pseudo-experiments showed that the case of High metallicity Sun and absence of $^{40}$K-geo-($\bar{\nu} + \nu$) can not imitate the result of multivariate fit analysis of Borexino Phase III data with introducing $^{40}$K-geo-($\bar{\nu} + \nu$) events. We also provide arguments for the high abundance of potassium in the Earth.
Comment: 17 pages, 7 figures. arXiv admin note: substantial text overlap with arXiv:2202.08531 We have corrected and expanded the section on radiogenic heat of the Earth. Improved the quality of drawings. The results of the study are partially described in L. B. Bezrukov, I. S. Karpikov, A. K. Mezhokh, S. V. Silaeva and V. V. Sinev, Bulletin of the Russian Federation. 87 (7), 972 (2023)