I would start with Reilly's service record.

These documents might be on Ancestry or Fold3 or other online places. You can also get service records directly from military archives.

Your aim is to find out:

1. The exact dates he was deployed.
2. The locations where he was in Germany (or other countries as borders have changed).

Continue to find everything you can about him.

It's possible he had contact with the children later on. Check census records (federal ones and state ones if available for his state) and city directories for others living at his address. Check for travel records showing he visited Germany. Ancestry often has this stuff and FamilySearch is another good resource.

Your eventual goal is to get enough information to find the children's birth certificates.

These might be online but more likely you'll need to hire a researcher. For this you need the town and a not-too-huge date range.

The interesting bit here is the word children.

That means he was in that location for at least a year, maybe longer. Even if the children in question were twins, you imply he was there when they were born so he could hand them over to the grandparents. Or he returned. He knew his partner died in childbirth, so this is not a case of him taking up with a local, getting her pregnant, then leaving.

Check for a marriage certificate.

You're not sure if they married. If they did, there will be a record. With online databases, you don't need to know the location before searching for a birth or marriage certificate. Chances are, however, that you'll need to search through online scanned reels of vital records or hire someone, so finding location and dates is crucial.

I would start with Reilly's service record.

Documents with some detail about the person's service might be on Ancestry or Fold3 or other online places. You can also get full service records directly from military archives.

Your aim is to find out:

1. The exact dates he was deployed.
2. The locations where he was in Germany (or other countries as borders have changed).

Continue to find everything you can about him.

It's possible he had contact with the children later on. Check census records (federal ones and state ones if available for his state) and city directories for others living at his address. Check for travel records showing he visited Germany. Ancestry often has this stuff and FamilySearch is another good resource.

Your eventual goal is to get enough information to find the children's birth certificates.

These might be online but more likely you'll need to hire a researcher. For this you need the town and a not-too-huge date range.

The interesting bit here is the word children.

That means he was in that location for at least a year, maybe longer. Even if the children in question were twins, you imply he was there when they were born so he could hand them over to the grandparents. Or he returned. He knew his partner died in childbirth, so this is not a case of him taking up with a local, getting her pregnant, then leaving.

Check for a marriage certificate.

You're not sure if they married. If they did, there will be a record. With online databases, you don't need to know the location before searching for a birth or marriage certificate. Chances are, however, that you'll need to search through online scanned reels of vital records or hire someone, so finding location and dates is crucial.