Say I have a group of people who live next to a volcano for religious reasons. They will not move. This volcano erupts very regularly - almost once a week. What kind of defence or adaptability strategy would my people use to cope with this regular disaster?
This is all also under a medieval 1300 technology, so they don't have much to work with.
For example, are there any rocks that can withstand volcanic lava so that my people can hide under it at every eruption?
Duel with Mother Nature long enough, and she will always win
This is important to understand. In 2018 humanity has not developed perfect defenses against any natural disaster. Not one. We have improved our survivability, but Mother Nature can always undo our efforts. So long as you're willing to live with this simple fact of nature (e.g., unless you want to bring magic into the mix), read on.
Trenches So long as eruptions are infrequent enough, one of your best defences is a big trench. Especially if that trench has a down-hill grade into the proverbial ocean (Go watch the movie Volcano starring Tommy Lee Jones). Your people will need time to clear the trench after every eruption.
An Absolutely Massive Basalt Breastwork In some ways this is unbelievable, unless there's a natural formation your people are hiding behind. Volcanism is powerful. One of the most powerful of the natural forces. A few rocks won't do. A 6-meter high wall might do... if it's at least 12-meters thick. Your problem is that molten rock is very good at helping solid rock become molten rock. Thus, man-made blockades are a bit hard to swallow. Your people will need to clear the solidified magma on the leading side of the wall after every eruption or each layer of magma will eventually smooth out the leading edge, turning the trailing edge (next to your city) into a watermagmafall.
Water Water can help, to a degree. If there's a big old river between you and the volcano, good for you! But given enough magma, rivers (and lakes) can be filled. You'll be dredging. But, a big river is as good as a trench, I say.
Off the top of my head, that's all you can do. Magma has the habit of going where it wants. Please don't forget what I said. There is no proof against volcanic eruption today — much less in the 1300s.
Edit:
Molot is right that I ignored a great many ways a volcano can kill a person. I consider Magma the easiest to defend against, and remember that my point is "mother nature will always win." If you can't defend yourself against magma, you can't defend yourself against anything else. Given 1300s tech, you can't hermetically seal a city. You might hermetically seal caves, suggesting your city is living in the caves, which would also protect you from falling debris ... except that on a volcano the caves are most likely lava tubes meaning you're either in the direct path of unstoppable magma or you're baking in an oven.
After thinking about it a bit more, the psychology that would bring a community to this point would include the risk of dying from the great power of the volcano. From that perspetive, creating a perfect defense (if such a defense is ever believable) would be to deny the power of your own god, so to speak. It would likely cause a schism in the faith.
If the volcano shows activity on a weekly schedule, it's very unrealistic that these people could survive. It's probably not the lava that kills them, but the toxic gases.
You could argue that the volcano has one active side where lava erupts regularily, while the people live on the inactive side. Similar cases can be seen on Hawaii. But there is no realistic way to protect an area from a lava flow. People have to give up their homes and build new ones in a (hopefully) safe place.
Depending on the chemical composition of the lava, the volcano releases clouds of ashes and toxic fumes as well as molten rock. Some of those fumes are heavier than air and creep over the landscape like an invisible avalance, suffocating or poisoning any living being in their wake. Because those gas streams cover wide areas, there's no chance of survival once you notice what's happening. A mild breeze could easily transport the gas from the active side to the (now formerly) inhabited side.
Lava getting in contact with water usually leads to the volcano emiting ashes. These cover and suffocate the vegetation and poison the livestock eating it together with plant material. The only benefit of volcanic ash is that it's very fertile ground for agriculture.
If your volcano does bot emit ashes, the hard, hot rocky ground does not permut agriculture for several decades or even centuries.
As others have said, the only real "defense" against a volcanic eruption is to be somewhere else.
You need to understand, however, that there are two distinct types of volcanos*. Stratovolcanos like Etna, Krakatoa, St. Helens (or Fuji, Shasta, & Rainier, to name a few that haven't erupted recently) tend to erupt infrequently but explosively. So you won't get a long period of weekly eruptions with this kind of volcano. People may live close to it for centuries, seeing occasional plumes from the vents - then one day it erupts, and they're all dead.
Shield volcanos like the ones that form the Hawai'ian Islands are different. They have a much more fluid lava, which tends to flow out of the volcano comparatively gently. Eruption cycles can last for a long time - Kilauea has been erupting since the 1980s - and don't necessarily cause much disruption to people. Worst case (as happened recently in Hawai'i), if the lava flow heads in the direction of your home, you have time to move elsewhere.
So if your volcano is of the shield type, your people can live quite well close to it, with nothing more than the occasional disruption. After all, Hawai'ians have been living with their volcanos for perhaps 1600 years.
*Four if you want to get technical, but cinder cones and lava domes don't really apply here: https://pubs.usgs.gov/gip/volc/types.html
They do not have to move because their religion is correct. By invoking the right powers, drawing the right sigils, erecting the right wards, and most importantly: making the right sacrifice, the god(s) intervene and divert the harmful effects of the eruption away from the settlement. Perhaps towards its enemies.
The sacrifices should be of something of value significant enough to justify the weekly avoidance of utter annihilation by way of divine intervention. Also, the villagers must have settled there for a very important reason which is tied typologistically to the form and content of sacrifice they have had to make every single week thereafter.
