CSS3 selector :first-of-type with class name?

No, it's not possible using just one selector. The :first-of-type pseudo-class selects the first element of its type (div, p, etc). Using a class selector (or a type selector) with that pseudo-class means to select an element if it has the given class (or is of the given type) and is the first of its type among its siblings.

Unfortunately, CSS doesn't provide a :first-of-class selector that only chooses the first occurrence of a class. As a workaround, you can use something like this:

.myclass1 { color: red; }
.myclass1 ~ .myclass1 { color: /* default, or inherited from parent div */; }

Explanations and illustrations for the workaround are given here and here.

The draft CSS Selectors Level 4 proposes to add an of <other-selector> grammar within the :nth-child selector. This would allow you to pick out the nth child matching a given other selector:

:nth-child(1 of p.myclass) 

Previous drafts used a new pseudo-class, :nth-match(), so you may see that syntax in some discussions of the feature:

:nth-match(1 of p.myclass)

This has now been implemented in WebKit, and is thus available in Safari, but that appears to be the only browser that supports it. There are tickets filed for implementing it Blink (Chrome), Gecko (Firefox), and a request to implement it in Edge, but no apparent progress on any of these.

I found a solution for your reference. from some group divs select from group of two same class divs the first one

p[class*="myclass"]:not(:last-of-type) {color:red}
p[class*="myclass"]:last-of-type {color:green}

BTW, I don't know why :last-of-type works, but :first-of-type does not work.

My experiments on jsfiddle... https://jsfiddle.net/aspanoz/m1sg4496/

This it not possible to use the CSS3 selector :first-of-type to select the first element with a given class name.

However, if the targeted element has a previous element sibling, you can combine the negation CSS pseudo-class and the adjacent sibling selectors to match an element that doesn't immediately have a previous element with the same class name :

:not(.myclass1) + .myclass1

Full working code example:

p:first-of-type {color:blue}
p:not(.myclass1) + .myclass1 { color: red }
p:not(.myclass2) + .myclass2 { color: green }

<div>
  <div>This text should appear as normal</div>
  <p>This text should be blue.</p>
  <p class="myclass1">This text should appear red.</p>
  <p class="myclass2">This text should appear green.</p>
</div>