If my last LMP was June 21st and my periods are normal 28-30 days.. What are the days I most likely conceived...

Anytime between June 22 and July 20. Sorry, but calculating conceptions dates is an inexact science. It can vary 2 weeks or more in either direction.

If this is a paternity issue and you had multiple partners during that time frame, then you will have to wait until the child is born and have a DNA test done to determine paternity.

I completely agree with Scott... if you are concerned about WHEN it happened exactly.. you will never knopw because tis impossible to determine medically. You will have to have a DNA test done after the child's birth if there is a question of which man is the father because you slept with more than one man that month..

June 21 - 25 I was on my period and I have a due date of March 28

That doesn't change anything... all that is , is a rough guess by the doctor.

Ovulation and conception, while sometimes relates to period dates, do not always, some women get pregnant while on period, some a week after period.

Unless you were tracking your ovulation schedule by medical means ( not online charts) there is no way to determine exactly when you got pregnant.

It occurred sometime in the 3 or 4 weeks, after your last period.

That is as close as you are going to get.

Is there an issue about a date?

June 21 - 25 I was on my period and I have a due date of March 28

Do you think that would change the answer? The only possible way to pinpoint conception is if you had ONE and only ONE sexual encounter between your last period and the time you found out you were pregnant. If you had multiple days where you had intercourse, then it could be any one of those days.

Were you taking your BBT every morning? (That's basal body temperature).

Do you KNOW, to the day, when you ovulated--based on your BBT?

If not, and you had sex multiple times that month (or if you DO, and had sex multiple times in the 3-5 days on either side of your ovulation), then there is no way to know.

If this is a matter of paternity, you need to get a DNA test done after the child is born.