Age is given partly as a continuous and partly as a categorical variable I have a dataset of the clinical information of 150 patients above 50 years old. I intend to do a logistic regression with it. (Presence of Symptom ~ Age, etc)
From 50 years old to 69 years old the ages are given continuously (50,51,52...68,69); from 70 years old the ages are given categorically/binned (70-74,75-79...95-99,100+)
I have 83 in the 50-69 yo group and 67 in the 70-100+ group.
How to know the best manner to proceed: Transforming the continuous data in categorical or the other way around?

You could impute the mean or median for each category. That would not work well for the 100+ but I suspect that unless there are many centenarians in your country imputing 100 would not do much harm. If you have the necessary programming skills you could impute for each category using a uniform drawn from 70-74, 75-79 etc, fit the model, repeat N times and see what difference it makes. I would not recommend doing that by hand.
I would not recommend categorising an essentially continuous variable unless there was no alternative. It wastes information and leads to a model which is implausible since it predicts the effect remaining flat through the category and then suddenly jumping to a new value at the category boundary.
In response to the information added in a comment by the OP that there were 7% in the 100+ category (which equals 10) it might be best to consider how to impute more sensibly there. If the country publishes detailed population statistics for those age groups then that would enable a picture of the actual distribution but I suspect that disclosure control would limit the detail at advanced ages. Although the upper limit of age is not known we can assume for practical purpose that it is 110. If we then assume that ages at this part of the range form a triangular distribution with lower limit 100, upper limit 110, and mode at 100 the estimated mean would be 103.3 so we could use that as our imputed value for age in the 100+ group.
