Search for very-high-energy photon clusters and transients outside the galactic plane in the Fermi-LAT data

We present a search for spatio-temporal clusters in 16 years of Fermi-LAT very high-energy (VHE; E>100 GeV) data using the DBSCAN algorithm, focusing on high Galactic latitude (|b|>10^) clusters with 5 events and transient doublets (two events within 3 days). Of 107 detected clusters, two correspond to previously unidentified VHE sources: weak BL Lacertae objects 4FGL J0039. 1-2219 and 4FGL J0212. 2-0219, promising targets for next-generation VHE observatories. Due to low VHE photon background, even doublets with a duration of several days exhibited high statistical significance. While most of the 114 detected doublets originated from bright TeV emitters (e. g. , Mrk 421, Mrk 501), we identified six VHE flares lacking TeVCat associations. Five of these flares correlate with sources from the Third Catalog of Fermi-LAT High-Energy Sources (3FHL), while one 'orphan' flare lacks a high-energy (HE; E > 10 GeV) source counterpart. Some of these flares reached extreme luminosities of O (10^47 erg~s^-1). No consistent temporal correlation emerged between HE and VHE activity: HE flares preceded, coincided with, or followed VHE emission across sources, with some showing no HE counterpart. Remarkably, 3FHL J0308. 4+0408 (NGC 1218) is a Seyfert Type I galaxy, while no object of this class was known VHE emitter before. The 'orphan' flare without any known HE source in the vicinity may originate from NGC 5549, a low-luminosity LINER galaxy. Both sources expand the limited sample of non-blazar AGN detected at VHE energies.