I planted basil at our backyard and at first, the leaves were healthy and smooth. but after 2-3 months, the new leaves that grew were wrinkled and looked ugly? is it due to over exposure to sunlight? i prefer not to use pesticide, and maybe is it beacuse of the insects? this could be the reason?

Get you a good plant food fertilizer. something has been depleted from the soil and without seeing the leaves I don't know what it is. Could be iron. Miracle Gro is like a multivitamin for a plant and will give it what it is missing. Next year plant your basil in a pot with potting soil. The soil in your yard may not be capable of growing anything but grass.

water it
check it for cut worms or aphids
fertilize it
cut the leaves and see if new ones appear

Check for nutrient deficiencies. You seem to have a problem with your plants cell retention, which can be caused by under/over watering but it seems like a fertilization problem. If you fertilize them often, you should cut down, if you haven't fertilized them, I think you should give it a try. Your soil may be running out of nutrients for the plants. You should look up plant deficiencies.

Could also be heat stress, but i cant suggest that being that i dont know which region you are in.

You're probably now seeing mature leaves . There are numerous varities of basil . Look at them and see if yours matches any crinkly ones . Dryness can make it more pronounced .

On the off chance it is a problem , gently blow on the plant . If you see a bunch of tiny , spearhead-shaped critters scurrying all over , you have thrips. Look on the undersides of the leaves . Any reddish dots, especially with webbing , red spider mite . A bunch of soft-bodied , little guys , all huddled together , maybe herded by ants, aphids . Go to local cooperative extension site, or similar for diagnosis & treatment options . Keep in mind stressed plants are more likely to attract pests. Also overfertilizing can lead to soft, vulnerable new growth that the pests love.

Scot-Rob , basil can be damaged by cold nights . It doesn't have to be freezing . Anything also wrong with cucumbers , or impatiens? If so, would be an indication that it was just the cold. Don't know the weather where you are, but here, in NYSt., it's just now safe for basil , & that's subject to change . Y'all might have put 'em out too early .

This is so weird, because this is happening to a lot of my plants right now and i don't know why (has never happened before). I am in UK and we had a very warm, dry April followed by a cooler, wetter May and I think this may be why some of my seedlings are doing this. If you've had a lot of weather changes recently this could be the reason...Basil likes warm and dry conditions so maybe it's too much rain all of a sudden?