If you are using a thick skinned root such as a Spanish black radish, plan to peel them prior to shredding. For thinner skinned turnips, just shred. If you are making larger batches a shred attachment on a food processor is especially helpful for getting the job done.
Place the shreds in a colander and toss with the salt. Allow it to rest for about 20 minutes, up to a few hours. The shreds will start to sweat and drip through the colander. When ready to use, squeeze the shreds with your clean hands until they are mostly dry. Skipping this step will add too much liquid to your fritters and they will steam rather than become crispy. At this point, try a bite of your shreds, if they taste to salty, rinse them well and squeeze again. Another easier way to squeeze the shreds is to place them in a thin dishtowel or cheesecloth, twist it up and wring out the excess liquid.
Once you have the nicely squeezed dried shreds, beat the egg and flour together until there are no flour clumps. It will be a thick almost paste-like batter. Fold in the root shreds and mix together well until the strands all seem to have some of the batter on them. There will be way more veggies than batter.
Warm the oil in a skillet over medium-low heat. Test the temperature of the oil by dropping a drip of batter in to the oil. It will start to sizzle immediately if it is hot enough, but if it burns too quickly lower the temperature slightly.
Once the oil is ready, bring together a small clump, anywhere from a tablespoon in size for mini-fritters to about a 1/4 cup dollop. Place the batter in the hot oil and sear for about 5-7 minutes. Flip over and sear on the other side. Place in an oven at about 200 degrees to keep them warm.
If making ahead, cool thoroughly before storing. Once it is time to cook them, spread them on a baking sheet and bake at 375 for about 10-15 minutes just before serving. Flip halfway through and bake until they are hot to the touch in the center.