Besides Spanish where you have comerla (feminine, eat her) or comerlo (masculine, eat him), but only works for certain verb conjugations.
Any other language where the gender of objects/subjects is marked in the verb conjugation?
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In the Northeast Caucasian languages, nouns are divided into classes, that category is analogous to the Indo-European and Semitic genders.
Let's take Archi, a Northeast Caucasian language. It has 4 noun classes: I. male, II. female, III. inanimate objects and adult animals, IV. abstract nouns and baby animals. Since Archi is an ergative language, the very idea of subject/object is different in it, all the verbs in Archi are marked for class – for the class of the "subject" with the intransitive verbs and for the class of the "direct object" with the transitive verbs. The same happens in all the languages of this language family.
I. vassar - [a man] shivers
II. dassar - [a woman] shivers
III. bassar - [a cow] shivers
IV. assar - [a calf] shivers
In the Bantu languages, like Swahili, there are also noun classes, but they are more numerous than in Archi (14 of them in Swahili), and the Swahili verbs are marked for the class of the subject, too.
In the Semitic languages I know about, gender is marked on subject and object verbal markers in the 2nd and 3rd person singular (when/if there is an object marker). Berber and various Chadic languages such as Somali do likewise, so it might be generally true of Afroasiatic. Khoekhoe also somewhat marks subject gender on the verb, though this is connected to movement.
In comerlo and comerla, the gender in not part of the conjugation! These are enclitic forms, where the object pronouns (lo, la,...) are written attached to the verb, but you can actually detach them and write it using a different word order: "Voy a verla" = "La voy a ver". This can, in principle, be done with all verbs, provided the pronouns are compatible, but only with infinitives and present participles. Semitic languages perfect example for what you're after.