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 $18.76pm0.14$ mag for NGC 419 and $18.86pm0.11$ mag for the SMC field, which agree with previous measurements.
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