Peel the shells off the tamarind, remove the stringy stuff, and put the tamarind pulp & seeds in a medium sauce pan.
1/2 lb dried tamarind pods
Add the sugar and only 3 cups of the water. Mix and cook over medium heat for 10 minutes or until it softens & thickens, then turn off the heat and cover with a lid for 1 hour.
1 1/2 cups sugar
After 1 hour, use your hands (wear gloves) to break down the pulp as much as you can. This will make it easier to push through a sieve.
Push through a sieve until there are mostly just the seeds left. You can throw these away.
This is what your tamarind pulp should look like. It's perfectly fine if it's thicker than this, but if it's too thin & doesn't coat your spatula, you need to cook it more.
Transfer to a pitcher or measuring glass, then add the remaining 1 cup of water. You may need a little less or more water, depending on your taste. Taste the mixture and make any adjustments for water & sugar. Tamarind is a very strong & overpowering flavor, so if you feel that it's too sour or too strong, you may need more water and/or sugar. *If using tajin and/or chamoy, you can mix it in now, or you can do it in the next step. I recommend anywhere between 2-4 tbsp of chamoy, and 1 tbsp of tajin.
tajin, chamoy
Pour into a clean popsicle mold, push in popsicle sticks, and freeze for at least 8 hours. *If using tajin and/or chamoy, you can layer it into the popsicle mold while pouring in the the tamarind mixture, alternating the ingredients 3-4 times. Then use a popsicle stick to gently swirl it around. This option is better than the previous one if you want to see a little bit of a swirly design in your paleta.
tajin, chamoy
For easy release, you can place the mold in warm water for 20 seconds, or use a popsicle stick to push down the sides of the paletas to loosen.
I recommend eating these within the first 2 weeks, but they can last much longer with a vacuum sealer and popsicle baggies. Keep in mind the longer they stay in the freezer, the more ice crystals will form!