I have seen conflicting information on this subject. From “The New Way To Learn Astrology” by Basil Fearrington, and The New A to Z Horoscope Maker and Delineator” by LLewllyn, both say that an interception has no special significance interpretively except for extending the timing of arcs or transits in a house.
This is due to the intercepted house being larger than the usual 30 degrees, so outer planets will take more time to move through them giving them more emphasis in the chart, through the lifetime.
Having said that Horary Astrology does give emphasis to interceptions in a chart, this is an area that is not expressed as well by the individual, and the energy may be more hidden here, more a 12th house emphasis.
I think it depends on what type of Astrology you are trying to work with as to how you interpret the interception of a sign.
The house that contains intercepted signs, that is all 30 degrees of the sign are within the boundaries of the house cusps. There will be an opposite intercepted sign in the house directly opposite, both equal and opposite in degrees. A polar balancing so to speak.
An intercepted sign will have two rulers of that house, the 1st and strongest ruler is the planet that rules the sign on the cusp of that house, the second ruler is the planet that rules the intercepted sign in that house. Look to the aspects of the rulers and how they are working in the chart to see how the house energy is being used. You have to look at both rulers for this and in some cases, both rulers are aspecting each other, or they deposit each other in house or sign.
Look to the planets in the house that contains the intercepted sign. Any planets in the sign of the interception are intercepted planets. There is more of a 12th house emphasis on these planets, that is they are used more internally, or their energy is hidden from view, this usually means a delay may be experienced in using this signs energy. You will have to move outside of this house, to find the tools to use this energy.