I supplied 12v to VIN pin to arduino uno and the area which I circled in the image started smoking. HOW should I repair this???
when I plugged it into a usb port it started heating up severely.
This is 3.3V DC regulator, LP2985-33DBVR on genuine R3 board. Similar in same package can be used. You have to replace it, but who knows if something else is not wrong.
12v on Vin shouldn’t matter. It should be connected to the barrel jack that can also accept 12v
It's better to use barrel jack because there is a diode in path which protects against reverse polarity. Just for future... 
I would be more concerned with reverse polarity of the barrel jack without knowing (realizing) than individual wires. Though wiring to the pins backwards also very possibly. Would it have been so difficult to connect Vin directly to the barrel jack? Though arrangement does prevent backfeeding of the barrel jack.
So should I replace the 3.3 voltage regulator???.The voltage regulator model is 4A2D.Or should I bouth a
LP2985-33DBVR. Thanks for replying.
See UNO schematics here on web. Original part is LP2985-33DBVR. The LD3985M33R 4A2D is probably some similar chinese part, but it doesn't matter. Any 3.3V LDO in SOT-23 should be fine. See this http://www.ti.com/lit/ds/symlink/lp2985.pdf. Similar according the parameters - LDO 3.3V, 150mA, SOT23.
Do not forget that there can be another problem, not only burned regulator. It can be just cause or result of another faulty part.
Thank you all for replying quickly. YOU saved me BUDVAR 10. Where can i buy it online?
When the atduino is plugged into a usb port it works fine . The sketch runs fine But the voltage regulator heats up. Would this damage the whole arduino uno board if it continues for a long time?
There is an electronic switch between USB and barrel jack (regulator).
If the regulator is heating (did you mean 5V or 3.3 ?) then something draws high current from it or it is damaged. In any case. try to repair it before next use.
Where to buy?
So, in any better shop with electronic parts. All depends on your location. Or, try internet shops like ali or ebay.
I meant 3.3 voltage regulator. 
Unless you get access to these parts cheap without the hassle of shipping costs, it may just as well be easier to buy another Uno for $7.25 from a USA seller on eBay.
.
Now I will ask the questions that have not been asked: What was plugged into the board? What external device was the 3.3V regulator powering?
As far as I can see in the schematic, there are no 3.3V powered components on the UNO board itself.
Usually when people smoke their boards by connecting external voltage to Vin, they accidentally got the polarity backwards.
It often takes out the regulators and sometimes the opamp used for the power supply switching - and on official boards and faithful clones, often the USB interface too.
Since Uno clones are so cheap, and often more than one component (all in surface mount packages) is damaged, it's hard to justify the time to repair them.
Ok thanks