Patterns can be re-colored by many means such as adjustment layers and adjustments in Photoshop
The first thing is to create a pattern or a pattern layer and that can be done in Photoshop in many ways such as using the layer menu and fill content and pattern content or using layer effects with a pattern overlay or using a fill via the edit menu and so on. You can also edit the color of the source pattern in Photoshop as well though that does require a few additional steps
You can find many patterns on this site such as flame and edge themed patterns and flower / rpsette seamless patterns and dot and spots patterns for Photoshop, psp, Affinity Photo etc
If you want to have a non destructive effect then the adjustment layers (layers menu) are probably best though if the pattern has been stored as a smart object then you can also use adjustments via the image menu and they are also then non destructive. If you don't mind radically and permanently changing the pattern then you can use the adjustments in the image menu. If you are using a pattern layer then you cannot use the image menu adjustments unless you flattern the work or change it into a smart object
If you go for the adjustment layers approach in Photoshop then you will have to select one of the adjustment layers such as channel mixer, photo filter, hue saturation etc and then you will see a properties panel appear where you can change the settings for the color of the underlying layer (or layers). Say, you decide to use the hue / saturation then you can then re-color or change the color such as hue / saturation / lightness. It should be noted that if the underlying layer is greyscale then the result of the hue etc will have no affect. You can set the panel adjustment layer to colorize which is a useful setting to change the entire pattern into blue or red etc Another great thing for changing the color of the patterns in Photoshop with adjustment layers is that you can add multiple adjustments (the same or different) and the layers can all be seen in the layers panel where they can be deleted or shifted up and down to modify the end result.
Another great thing about using the adjustment layers to modify the patterns is that you can click the properties panel and instead of the hue / saturation you can select the mask (at the top of the panel with the little frame icon) and then you can modify only a part of the underlying pattern and you can then go to the layers panel and add or subtract from the mask to see more or less of the changes to the color of the pattern.
With adjustment layers and patterns in Photoshop, you can also use blending modes with the adjustment layers so the adjustment can be radically changed by using linear burn or difference etc via the layers panel for the adjustment layer (or layers if you have more than one)
You can also add a selection to the pattern beforehand and then use a selection to define a particular area to be adjusted and that adjustment layer can be a lot less than the original pattern size (perhaps circles or dots or a square etc) and the adjustment can then be selected and shifted as as re-sized or rotated etc as well as duplicated and then used to create interesting color shifts on top of the Photoshop pattern. You can also use the pen tool as a great way of creating an interesting shape for your adjustment layer, select path mode with the pen tool and just add the anchor points and go to the path panel and create a selection from the right side menu and then invert and then apply the adjustment layer and you will see only that part of the image change and as it is a layer, you can then move the artwork around and re-size and also adjust the settings for the color as well as use different blending modes (see the video at the bottom of the page showing an example)
You don't have to use the patterns as a layer as well as the adjustments in Photoshop, just flatten and then re-color the pattern using the image menu adjustments and the range of options is slightly greater as now you can use the HDR toning which adds even more amazing colorful manipulation to the pattern. You can apply the adjustment multiple times (the same or different adjustments)
You can also edit the original source patterns from the patterns panel in Photoshop and use adjustments and adjustment layers with that to make a permanent change to the color. You need to find the pattern dimensions by hovering over the pattern in the panel and if it is 2000 x 2000 for the source tile then create a document with that set of dimensions and use the edit menu and fill. You can then use adjustments such as hue / saturation and in most cases, the results should still be a seamless tile. You can then go to the edit menu and define the pattern again.
You can find many other tutorials on the site such as how to create an exciting pyramid pattern in Photoshop and how use lines and pattern tools in Photoshop to create unique backgrounds and textures and how to copy patterns from Photoshop for use in other apps such as Affinity Photo tutorial