Were there any round shields used, from the 12th century onward? Were there any handheld, as opposed to strap and carry, type shields present in that period? By whom? Thank you for your time.
Yes and yes. I'll stick to western Europe for this answer, as I'm not really comfortable with interpreting Byzantine artistic conventions.
The 'buckler' was a very common shield for both civilian (late 13th c.) and military contexts from about the timeframe of your question until around the 16th century when it was supplanted for civilian duels by a parrying dagger, and in military use by pikes and firearms. It was held by a central grip, fairly small, and usually of entirely metal construction. The shield that the 'Rodeleros' of 16th century Spanish armies used is often referred to as a 'buckler' in English, but it was a fair bit bigger than most of the medieval examples (I don't read Spanish, so I just linked the last page for the pictures. You can see some of the shields seem to have a central handle, while others are strapped to the arm).
Larger round shields are mostly used in medieval art to show 'foreignness' of some kind, for instance Muslims or Philistines, but there are a few works that show them in a more European setting 2.
Round 'targes'/'targets' also survived in Scotland until the 18th century though they were strapped to the arm rather than held by a handle.
EDIT: I just saw the other version of this question that you posted, sorry this probably wasn't very helpful. Here's the closer stuff I found. The twelfth century Eadwine Psalter has round, centre-grip shields, but the illustrations are adapted from a ninth-century work. This picture seems to show a kite shield with a central grip, but the angle's funny. The round shield tag on the manuscript miniatures site gives a bunch of interesting results, but a lot of them don't seem to be representing Europeans. Some of the better ones I thought were from this Spanish bible, though they are strapped to the arm, and in some cases only carried by one of the armies (so presumably 'foreign'), this English one (though it may be a not-to-scale buckler), and this picture from the Morgan Bible (I have one from the Morgan bible further up, but this one is carried by a soldier on the Israelite side, which is usually less fancifully drawn). There are some other interesting ones there, but most seem to be carried by the 'pagan' armies.
