History knows certain periods in the history of nations, when distinctions were made between men’s, women’s, and children’s crosses. For example, such beliefs existed among some Old Believer communities in the 18th and 19th centuries. But all this must be attributed to local customs, and not to the rules of the Church.
Canonically, in the Orthodox Church there is no distinction between crosses in age and sex, since “in Christ there is no Hellen, no Jew, no man, no woman,” according to the Gospel. But since crosses are honored and produced in the most diverse forms and in iconography, no one forbids himself and his child to choose a cross, guided by personal ideas and tastes. There are no separate baptismal crosses. You can be baptized by any canonical cross.