We report the results of $1^{prime}.5 times3^{prime}$ mapping at 1.1~mm with the Atacama Large Millimeter/submillimeter Array (ALMA) toward the central region of the $z=3.09$ SSA22 protocluster. By combining our source catalog with archival spectroscopic redshifts, we find that eight submillimeter galaxies (SMGs) with flux densities, $S_{rm 1.1~mm}=0.7-6.4$~mJy ($L_{rm IR}sim10^{12.1}-10^{13.1}L_odot$) are at $z=3.08-3.10$. Not only are these SMGs members of the protocluster but they in fact reside within the node at the junction of the 50 Mpc-scale filamentary three-dimensional structure traced by Lyman-$alpha$ emitters (LAEs) in this field. The eight SMGs account for a star formation rate density (SFRD) $sim$10 $M_odot$ yr$^{-1}$ Mpc$^{-3}$ in the node, which is two orders of magnitudes higher than the global SFRD at this redshift. We find that four of the eight SMGs host a X-ray luminous active galactic nuclei (AGN). Our results suggest that the vigorous star formation activity and the growth of super massive black holes (SMBHs) occurred simultaneously in the densest regions at $zsim3$, which may correspond to the most active historical phase of the massive galaxy population found in the core of the clusters in the present universe. Two SMGs are associated with Lyman-$alpha$ blobs (LABs), implying that the two populations coexist in high density environments for a few cases.
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