What is the word/name I am looking for; regarding twins?

It sounds like you may be “ Polar Body Twins “ sometimes referred to as “Half Identical” Twins I quote the following: “… There are two types of twins, right? Dizygotic (fraternal) twins result when two eggs are fertilied. Monozygotic (identical) twins come from a single fertilized egg that splits. But what if the egg splits and then each half meets a sperm? That’s the proposed theory for polar body or “half-identical” twins, twins who are very much alike but aren’t a 100% DNA match. Although it seems to be a reasonable theory, there is no definitive test to confirm polar body twinning. …” From http://funadvice.com/r/14pj7b1bb2a

which describes 10 unusual types of twins, in which “Polar Body Twins” are listed at number 4

– Best wishes - Majikthise.