  Delta Scuti ($\delta$ Sct) stars have been extensively studied in our Galaxy,
but far less in extragalactic systems. Here we study the population of $\delta$
Sct variables in NGC 419, an intermediate-age globular cluster of the Small
Magellanic Cloud (SMC), using $g,r,i$ Gemini-S/GMOS time series observations.
Our goal is to study the role of such variables in the cluster extended
main-sequence turnoff (MSTO). We report the discovery of 54 $\delta$ Sct stars
and three eclipsing binaries in the NGC 419 field. We find only a handful of
the $\delta$ Sct stars at the MSTO of NGC 419 while the majority is fainter,
indicating that the cluster is younger ($\lesssim 1.2$ Gyr) than previously
thought. Considering their radial distribution, we identify only six $\delta$
Sct stars as probable members of NGC 419 while the 48 remaining are likely
$\delta$ Sct stars of the SMC field. Cluster $\delta$ Sct stars appear close to
the red edge of the MSTO, supporting the idea that the extended MSTO has its
origin in an age spread. The 48 field $\delta$ Sct stars represent the largest
detection of $\delta$ Sct stars made in the SMC. The period distribution of
these newly detected $\delta$ Sct stars ($0.04 \lesssim P \lesssim 0.15$ d) is
similar to that detected in other systems. The amplitude distribution ($0.05
\lesssim \Delta r \lesssim 0.60$ mag) is likely biased because of the lack of
low-amplitude stars. We finally use the $\delta$ Sct stars to calculate
distances using different period-luminosity relations. The average distance
moduli obtained are $18.76\pm0.14$ mag for NGC 419 and $18.86\pm0.11$ mag for
the SMC field, which agree with previous measurements.
