I am working on data regarding Vitamin D deficiency among newborn babies in relation to variables such as gestational age and birth weight. The sample consists of 88 babies (49 male and 39 female babies) with different gestational ages and birth weights. I wanted to see if there is correlation between baby Vitamin D level and these variables so I used bivariate correlation test for Vitamin D and gestational age, then for Vitamin D and birth weight and there was positive correlation in both tests, but now I want to control the effect of each of gestational age and birth weight individually to find the pure correlation of each one of them, i.e., I control gestational age to find the pure correlation between Vitamin D and birth weight, then I control birth weight to find the pure correlation between Vitamin D and gestational age, is partial correlation the suitable test or not? and what if I want to control the effect of sex of baby? what test should I use?
As Nick Cox posted in the comments, using a regression model seems like it is likely appropriate based on your comments.
Since you can't actually control the the level of the independent variables that you're working with, starting out with a correlation model was fine; however, I would bet that vitamin D levels and birth weight follow a bivariate normal distribution. If so, regression is an appropriate next step.
Gestational age is a bit different. It can't follow a normal distribution since normal distributions allow for negative numbers. If we're measuring live births, then maybe gestational age can be approximated by a normal distribution, but that's something you'd have to determine yourself. If it is, then you could also try regression on it as well.
The way you phrased your question,
I control gestational age to find the pure correlation between Vitamin D and birth weight, then I control birth weight to find the pure correlation between Vitamin D and gestational age
makes it sounds like you want to make two separate simple OLS (ordinary least squares) regression models. I would recommend instead using multiple regression with birth weight as your dependent variable and vitamin D levels + gestational age as your independent variables.
If you want to control for sex, you can add a dummy variable. This means, for example, male babies are coded 1 and female babies are coded 0. When you perform your regression, you can then see how much impact sex is having on birth weight.
The test you would use on the individual variables to determine their significance is the t-test.