There are presently no journals devoted exclusively to exposome studies or exposomics, however "exposure science" is a broader classification under which these fall; these journals publish content in these areas:
Books free online.
Books linked below are available online or via the University Library.
PubMed results for a title keyword search: exposome [ti] OR exposomics [ti]. There is currently no Medical Subject Heading (MeSH term) for this concept.