Firstly, it is likely that there is a reverse causality between economic growth and debt (public or private?). This can cause an endogeneity problem in most models. Hence, it would be useful to apply Granger causality first to see the direction of the causality in Granger sense. Then you can try to use fixed-effect or random-effects models based on your panel data to find a short-run effect. However, I would also recommend you testing for potential long-run effect by panel cointegration test (if both variables are non-stationary at their levels). Then you can use VECM. If there is no cointegration you can use VAR models for short-run causality and controlling for reverse causality.

The right model depends on your data, according to yours I guess dynamic panel data would fit like mentioned above, and for long run causality VECM or ARDL would fit, ARDL can be applied even if you have variables integrated in different orders. And for short run causality you can use Granger causality.

@Jan Hunday @Ayoub Rabhi

Sir three main variables; Total External debt, Public External debt and private External debt