  We use JWST/NIRCam medium band photometry in a single pointing of the
CAnadian NIRISS Unbiased Cluster Survey (CANUCS) to identify 118 Extreme
Emission Line Galaxies (EELGs) over $1.7 \lesssim z \lesssim 6.7$, selected
using a set of color cuts that target galaxies with extreme $\text{[OIII] +
H}\beta$ and H$\alpha$ emission. We show that our medium band color selections
are able to select galaxies based on emission line equivalent width (EW), which
is advantageous to more commonly used selections since it does not require
strong continuum emission, and can select galaxies with faint or red continuum
fluxes. The median EWs of our sample is $EW(\text{H}\alpha) = 893 $ \AA\ and $
EW(\text{[OIII] + H}\beta) = 1255 $ \AA, and includes some objects with
$EW(\text{[OIII] + H}\beta) \sim 3000$ \AA. These systems are mostly compact
with low stellar mass (median $\log(M_\star/M_\odot) = 8.03$), low metallicity
(median $Z = 0.14 Z_\odot$), little dust (median $A_V = 0.18$ mag) and high
SSFR (median $SSFR = 1.18 \times 10^{-8}/yr$). Additionally, galaxies in our
sample show increasing EW(\Ha) and EW(\OIIIHb) with redshift, an
anti-correlation of EW(\Ha) with stellar mass, and no correlation between
EW(\OIIIHb) and stellar mass. Finally, we present NIRSpec spectroscopy of 15 of
the EELGs in our sample. These spectra confirm the redshifts and EWs of the
EELGs calculated from the medium bands, which demonstrates the accuracy and
efficiency of our color selections. Overall, we show that there are significant
advantages to using medium band photometry to identify and study EELGs at a
wide range of redshifts.
