  Context. The Optical Gravitational Lensing Experiment (OGLE) observed around
450,000 eclipsing binaries (EBs) towards the Galactic Bulge. Decade-long
photometric observations such as these provide an exceptional opportunity to
thoroughly examine the targets. However, observing dense stellar fields such as
the Bulge may result in blends and contamination by close objects.
  Aims. We searched for periodic variations in the residual light curves of EBs
in OGLE-IV and created a new catalogue for the EBs that contain `background'
signals after the investigation of the source of the signal.
  Methods. From the about half a million EB systems, we selected those that
contain more than 4000 data points. We fitted the EB signal with a simple model
and subtracted it. To identify periodical signals in the residuals, we used a
GPU-based phase dispersion minimisation python algorithm called cuvarbase and
validated the found periods with Lomb-Scargle periodograms. We tested the
reliability of our method with artificial light curves.
  Results. We identified 354 systems where short-period background variation
was significant. In these cases, we determined whether it is a new variable or
just the result of contamination by an already catalogued nearby one. We
classified 292 newly found variables into EB, $\delta$ Scuti, or RR Lyrae
categories, or their sub-classes, and collected them in a catalogue. We also
discovered four new doubly eclipsing systems and one eclipsing multiple system
with a $\delta$ Scuti variable, and modelled the outer orbits of the
components.
