Well i got 2 ways through which you could easily get your Recent Posts widget for blogger.
Just Follow The Steps
Let’s Start With Number 1:
1. First get your feed address of your post. Usually it is something like this:
http://YOUR_WEBSITE.com/feeds/posts/default
2. Copy it and then go to blogger dashboard, click the Layout button of your blog
4. Their scroll down and search Feed
5. Type your Feed link.
Your post would be automatically updated in that gadget you added.
Now the Number 2 (You need feedburner for it):
1. Login your feedburner account.
2. Select your bloggers feed stat dashboard.
3. Click “PUBLICIZE” in upper tabs
4. In left bar click “BUZZ BOOST” and activate it.
5. Select the settings you like
6. Then post that code in your blog.