  Foreground removal is one of the biggest challenges in the detection of the
Cosmic Dawn (CD) and Epoch of Reionization (EoR). Various foreground
subtraction techniques have been developed based on the spectral smoothness of
foregrounds. However, the sources with a spectral peak (SP) at Megahertz may
break down the spectral smoothness at low frequencies (< 1000 MHz). In this
paper, we cross-match the GaLactic and Extragalactic All-sky Murchison
Widefield Array (GLEAM) extragalactic source catalogue with three other radio
source catalogues, covering the frequency range from 72 MHz to 1.4 GHz, to
search for sources with spectral turnover. 4,423 sources from the GLEAM
catalogue are identified as SP sources, representing approximately 3.2 per cent
of the GLEAM radio source population. We utilize the properties of SP source
candidates obtained from real observations to establish simulations and test
the impact of SP sources on the extraction of CD/EoR signals. We statistically
compare the differences introduced by SP sources in the residuals after
removing the foregrounds with three methods, which are polynomial fitting,
Principal Component Analysis (PCA), and fast independent component analysis
(FastICA). Our results indicate that the presence of SP sources in the
foregrounds has a negligible influence on extracting the CD/EoR signal. After
foreground subtraction, the contribution from SP sources to the total power in
the two-dimensional (2D) power spectrum within the EoR window is approximately
3 to 4 orders of magnitude lower than the CD/EoR signal.
