You are correct that the ASEC oversample consists of the Hispanic oversample and SCHIP oversample. There is no variable that explicitly identifies the oversample group of these additional observations. The SCHIP oversample is first introduced in 2001, so there won’t be any cases in 1978-1982. In 2015-2019, households that do not include anyone who is Hispanic and do include someone under the age of 18 are likely the SCHIP oversample households.
Note, the SCHIP oversample does not result in additional variables , only additional observations for the variables already included as part of the ASEC. The SCHIP oversample was added to produce reliable state-level estimates on low-income children and measure the effects of SCHIP; while some research questions may justify handling these cases separately (e.g. linking CPS to leverage the panel component of the data), they are intended to be used alongside the standard sample.
You can find more information on the oversamples as they relate to linking CPS observations in section 2c of the working paper “Using the Annual Social and Economic Supplement with Current Population Survey Panels” from our colleagues Sarah Flood and Jose Pacas.