DNA replication stress promotes cancer development and is associated with DNA synthesis beyond S-phase. Replication stress-induced DNA lesions and under-replicated DNA can persist into G2 and mitosis, where they undergo mitotic DNA synthesis (MiDAS). After cell division, inherited DNA lesions are protected by genome caretaker proteins and show signs of post-mitotic DNA synthesis (post-MiDAS) in G1. The genomic regions that undergo post-MiDAS, the cellular factors involved, and the implications for genome integrity remain poorly understood. Here, we provide evidence for post-MiDAS activity at centromeres and telomeres in cancer cells employing alternative lengthening of telomeres (ALT) and present data suggesting that a subset of these fragile genomic regions can cluster during post-MiDAS in G1. We further show that post-MiDAS is promoted by local SUMOylation and BLM recruitment into ALT-associated PML bodies (APBs) and involves DNA damage tolerance factors and proteins associated with ALT and MiDAS. Consistent with G1-specific regulation, complementary quantitative proteomics and targeted siRNA screening reveal that APC/C, together with its G1 co-activator CDH1 but independent of its mitotic co-activator CDC20, restrains excessive post-MiDAS in G1. Finally, we show that CDH1 depletion selectively impairs the survival of ALT-positive cancer cell lines, indicating that post-MiDAS might represent a potential ALT-specific vulnerability. This dataset contains RPA70 immunoprecipitation mass spectrometry data generated from whole-cell protein extracts of FACS-sorted G1-phase U-2 OS FUCCI cells to identify the interactome of RPA70 in G1.