I am using windows 10. My laptop screen resolution is 1080p. However I want to record the screen (along with the system audio), such the the screen recording is done in a custom resolution(say 360p). I don't want to first record in 1080p and then scale it down. Can you suggest a free software that can do the job? An open-source recommendation will be more preferred.
OBS Studio, a free, multi-platform screen capture/streaming/video editing program appears to do as you require.
From a photography/video tutorial site, this specific screen shows that the program can be configured as you request:
As shown in the image, the input and output resolutions are adjustable, as is the output frame rate and the algorithm for downscaling the video.