  We present an analysis of 102 type Ia supernovae (SNe Ia) in nearby (z <
0.1), x-ray selected galaxy clusters. This is the largest such sample to date
and is based on archival data primarily from ZTF and ATLAS. We divide our SNe
Ia into an inner cluster sample projected within $r_{500}$ of the cluster
center and an outer cluster sample projected between $r_{500}$ and
$2\,r_{500}$. We compare these to field samples of SNe Ia at similar redshifts
in both quiescent and star-forming host galaxies. Based on SALT3 fits to the
light curves, we find that the inner cluster SNe Ia have a higher fraction of
fast-evolving objects (SALT3 $x_1 < -1$) than the outer cluster or field
quiescent samples. This implies an intrinsically different population of SNe Ia
occurs in inner cluster environments, beyond known correlations based on host
galaxy alone. Our cluster samples show a strongly bimodal $x_1$ distribution
with a fast-evolving component that dominates the inner cluster objects
($\gtrsim$ 75%) but is just a small fraction of SNe Ia in field star-forming
galaxies ($\lesssim$ 10%). We do not see strong evidence for variations in the
color (SALT3 $c$) distributions among the samples and find only minor
differences in SN Ia standardization parameters and Hubble residuals. We
suggest that the age of the stellar population drives the observed
distributions, with the oldest populations nearly exclusively producing
fast-evolving SNe Ia.
