Context. Quiet-Sun Ellerman bombs (QSEBs) are small-scale magnetic reconnection events in the lower solar atmosphere. Sometimes, they exhibit transition region counterparts, known as ultraviolet (UV) brightenings. Magnetic field extrapolations suggest that QSEBs can occur at various locations of a fan-spine topology, with UV brightening occurring at the magnetic null point through a common reconnection process. Aims. We aim to understand how more complex magnetic field configurations such as interacting fan-spine topologies can cause small-scale dynamic phenomena in the lower atmosphere. Methods. QSEBs were detected using k-means clustering on Hβ observations from the Swedish 1-m Solar Telescope (SST). Further, chromospheric inverted-Y-shaped jets were identified in the Hβ blue wing. Magnetic field topologies were determined through potential field extrapolations from photospheric magnetograms derived from spectro-polarimetric observations in the Fe I 6173 Å line. UV brightenings were detected in IRIS 1400 Å slit-jaw images. Results. We identify two distinct magnetic configurations associated with QSEBs, UV brightenings, and chromospheric inverted-Y-shaped jets. The first involves a nested fan-spine structure where, due to flux emergence, an inner 3D null forms inside the fan surface of an outer 3D null with some overlap. The QSEBs occur at two footpoints along the shared fan surface, with the UV brightening located near the outer 3D null point. The jet originates close to the two QSEBs and follows the path of high squashing factor, Q. We discuss a comparable scenario using a 2D numerical experiment with the Bifrost code. In the second case, two adjacent fan-spine topologies share fan footpoints at a common positive polarity patch, with the QSEB, along with a chromospheric inverted-Y-shaped jet, occurring at the intersection having high Q values. The width of the jets in our examples is about 0″.3, and the height varies between 1″–2″. The width of the cusp measures between 1″–2″. Conclusions. This study demonstrates through observational and modelling support that small-scale dynamic phenomena, such as associated QSEBs, UV brightenings, and chromospheric inverted-Y-shaped jets, share a common origin driven by magnetic reconnection between interacting fan-spine topologies.