I am finding a problem in understanding the sign convention associated with measuring the dip angle (Magnetic Inclination) in southern and northern hemisphere. I have tried to consult this matter on several books and found contradictory text.
By definition, the dip (inclination) is positive downwards (into the Earth) and negative upwards. See, for example, this page from the National Centers for Environmental Information and this book. (I wonder what books you read - I have never seen it defined any other way.) Since the Earth's field dips down in the northern hemisphere, its inclination is positive; and in the southern hemisphere, it is inclined upwards (negative).
Angle of dip in northern hemisphere is taken as positive and in southern hemisphere it is taken as negative