Hello @Gago - welcome to our community!
If your asylum application ends with a negative result there is still a chance for you to get asylum through your children - even if you are not married to your fiancé and if your children are illegitimate. In this case it is important that you do a so-called “Vaterschaftsanerkennung” (acknowledgement of paternity) and that you prove that you take care of your children (child custody). This way you can get a so called “Aufenthaltserlaubnis zur Personensorge”. The source that I found recommends to get in touch with an experienced lawyer or a counseling center to check if it works in your specific case though.
For further information about this topic please also check out the following link. We discussed a similar topic there: https://www.wefugees.de/k/questions/2216
Source (German language): https://www.nds-fluerat.org/leitfaden/8-perspektiven-nach-negativem-abschluss-eines-asylverfahrens/62-aufenthaltsrecht-aus-anderen-gruenden/
If your appeal ends with a negative result and you get deported, chances to get here through family reunion are quite low. Usually it is possible for children under 18 that are recognized refugees to get reunited with their parents (if they didn't flee with them). But as far as I found out this only works if none of the parents are here yet. In your case the mother is already with the children which probably builds ground for Ausländerbehörde to deny family reunion.
Source (German language): https://www.berlin.de/willkommenszentrum/familie/nachzug-von-familienangehoerigen/
I hope this answer was helpful to you.
Maybe @Marcel and @Steven can add some information.