If i had an older home without soffits i would strongly consider just completely air sealing the attic and adding foam insulation totally removing the need for ventilation.
Venting attic without soffit access.
Normal vented air likes to enter the attic lower down near the bottom third of the attic and as it passes through it will exit higher up near the top third of the attic space.
Typically you would have a gable vent on each end of the attic.
Install special roof intake venting products that work at the lower edge of the roof decking underneath the first course of shingles.
Problems when roof has no overhang.
The design of many older houses omits eaves which maximizes the amount of sunlight.
With old homes it can be very difficult to properly ventilate the attic for a variety of reasons.
One great alternative to a soffit ventilation system is to install an intake vent right at the lower edge of the roof.
This method relies on convection which is a mode of heat transfer that is caused by the tendency of warmer air to rise.
The most common method is the static method.
For proper ventilation it isn t enough for air to simply get into your attic.
Venting solutions for roofs with no overhang or soffit.
The venting drip edge seems to be the easiest and most common way to go.
They call this a venting drip edge.
How to vent an attic with no eaves the function of soffit vents.
Smart vent a special roof eaves vent product that provides a 3 4 opening about 6 above the top of the roof drip edge.
In other words air flows through the attic space naturally without the use of mechanical means.