How to Remove Garlic Ginger Paste smell from refrigerator
For the future, the only effective way I know of is to seal it doubly. That is, take two containers that promise to be airtight (such as glasslock style containers with gaskets), keep the paste in the inner one, and the inner one in the outer one. I know this is very tedious, but I have not found any other way that works for garlic smells in a fridge. Try using glass or steel containers, since plastic is permeable after some time, and also binds with the smell. 

If your fridge stinks now, you have to clean it out thoroughly. Throw out whatever food has taken on the smell, you cannot remove it. Wash the shelves, preferably in a dishwasher at a "pots" cycle. Turn off the refrigerator, wash it with something strong - I suggest 12% hydrogen peroxide, this also kills mold spores if there are any - and let it air for half a day until you return the shelves and food and turn it on again.