All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
Having children is a common right to both spouses (and neither of them has the right to prevent the other from it without a sound excuse). The husband has no right to deny his wife her right to having more children. Please refer to fatwas 82274 and 92181.
If the seven children in reference were born out of wedlock, as mentioned, then, according to the majority of the scholars, they are not attributed to the biological father. Rather, the illegitimate children are attributed to their mother only, as underlined in fatwa 117362. Some scholars, though, held that if the biological father acknowledges paternity and wishes to attribute them to himself, they are attributed to him. We give preponderance to the opinion of the majority of the scholars in this regard.
In any case, this man's wife is not obliged to do anything for these children unless she willingly chooses to raise them and care for them.
It should be stressed that a Muslim must beware of adultery, as one of its worst evils is getting illegitimate children, who might lead an unstable, insecure life that inevitably affects their future.
Allah knows best.