The factor that could increase the possibility of mutations in your offspring is having a mutation on a non-gamete cell. However, it is important to note that only mutations in gametes (sperm or egg cells) can be inherited by offspring. If a mutation occurs in non-gamete cells, it won't directly affect the genetic material passed to offspring. But certain environmental factors like smoking tobacco can increase the rate of mutations in gametes, which could influence the likelihood of passing on mutations.
If the context of the question is focused solely on the genetic transmission to offspring, mutations must occur in the germ cells (gametes) to be inherited.