Start heating the cooking oil in a pan. Ideally, the depth of the oil should be at least three inches. The ideal frying temperature is 350F to 375F.
Peel the onions. Cut into half-inch rounds. Separate into rings. Toss with half of the paprika and half of the cayenne.
Make the batter. Whisk the remaining paprika and cayenne with the flour. Pour in the vodka. Slowly pour in the beer while whisking at the same time.
Dump the onion rings into the batter. Mix thoroughly to coat each piece with batter.
Test the temperature of the oil by dropping in one onion ring. It should float and crackle, and bubbles should form around it. If the onion ring sinks and does not float within two seconds, the oil is not hot enough. If it browns within seconds, the oil is too hot. Make the necessary adjustments.
Drop the beer-battered onion rings in the hot oil one by one. Do this in batches to prevent overcrowding the pan. Overcrowding will make the temperature of the oil drop and that will result in soggy rather then crispy onion rings. Fry for one to two minutes or just until browned and crisp.
As each batch finishes cooking, scoop out and move to rack or a strainer. Proceed with the next batch, and so on.
Sprinkle the beer-battered crispy onion rings with salt and serve immediately with your preferred dipping sauce.