PREPARE THE DIPPING SAUCE
1-Heat oven to 375 degrees, put garlic: Heat oven to 375 degrees, put garlic cloves in a small baking dish and add enough olive oil to cover. Roast until garlic is soft and golden, about 30 minutes. Cool.
2-Drain garlic, reserving oil: Drain garlic, reserving oil. Transfer to a food processor, add 1 tablespoon reserved oil and the mayonnaise, lemon juice, salt and pepper and purée. Transfer to a bowl and stir in chives. Use remaining oil for another purpose.

PREPARE THE FRITTERS
3-Combine flour, Cheddar, salt, pepper and garlic: Combine flour, Cheddar, salt, pepper and garlic powder in a large bowl. In a separate bowl, gently whisk eggs with beer. Pour egg mixture into flour mixture and stir until combined. Stir in zucchini, yellow squash and onion.
4-Heat canola oil in a large heavy-bottomed: Heat canola oil in a large heavy-bottomed skillet over medium-high heat. Drop about 1 tablespoon of batter into the oil per fritter and fry 6 fritters at a time until golden-brown, 2 to 3 minutes a side. Remove to paper towels to drain. Serve hot, with the sauce on the side.