Fitting of continuous transfer function
You'll be jumping down the rabbit hole of system identification and modelling. Generally speaking you will need two things:

The first is a so-called estimator (wiki), that you can use to find the best "fit" of a general rational transfer function. The ones I've encountered most are


Least-Squares Estimator
Maximum-Likelihood Estimator (wiki)


They work by defining a cost function that you try to minimize using the unknown tranfer function coefficients. For the least-squares estimator, the cost function is simply the sum of the squared errors.

The second one is a model selection criterion (wiki). In order to avoid modelling the noise of your data points, you can use this criterion to formally find the optimal model complexity (order of the system).